LMFDB - Embedded newform 234.2.z.a.41.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.958654 - 1.44256i) q^{3} +(0.866025 - 0.500000i) q^{4} +(3.32591 - 0.891175i) q^{5} +(1.29935 + 1.14529i) q^{6} +(-0.0201488 - 0.0201488i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.16197 + 2.76583i) q^{9} +(-2.98193 + 1.72162i) q^{10} +(-1.12616 - 4.20290i) q^{11} +(-1.55150 - 0.769968i) q^{12} +(1.39839 + 3.32333i) q^{13} +(0.0246771 + 0.0142473i) q^{14} +(-4.47397 - 3.94350i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.35521 - 5.81139i) q^{17} +(0.406522 - 2.97233i) q^{18} +(-0.521462 - 1.94612i) q^{19} +(2.43473 - 2.43473i) q^{20} +(-0.00975013 + 0.0483815i) q^{21} +(2.17558 + 3.76822i) q^{22} +0.528142 q^{23} +(1.69792 + 0.342174i) q^{24} +(5.93735 - 3.42793i) q^{25} +(-2.21088 - 2.84816i) q^{26} +(5.10381 - 0.975270i) q^{27} +(-0.0275237 - 0.00737496i) q^{28} +(-7.19404 - 4.15348i) q^{29} +(5.34218 + 2.65118i) q^{30} +(-0.373424 - 1.39364i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-4.98334 + 5.65369i) q^{33} +(-1.73678 + 6.48176i) q^{34} +(-0.0849690 - 0.0490569i) q^{35} +(0.376625 + 2.97627i) q^{36} +(-2.09857 + 7.83198i) q^{37} +(1.00739 + 1.74484i) q^{38} +(3.45354 - 5.20318i) q^{39} +(-1.72162 + 2.98193i) q^{40} +(3.55302 + 3.55302i) q^{41} +(-0.00310415 - 0.0492564i) q^{42} +8.76179i q^{43} +(-3.07674 - 3.07674i) q^{44} +(-1.39975 + 10.2344i) q^{45} +(-0.510146 + 0.136693i) q^{46} +(-0.775777 - 0.207869i) q^{47} +(-1.72862 + 0.108938i) q^{48} -6.99919i q^{49} +(-4.84783 + 4.84783i) q^{50} +(-11.5998 + 0.731018i) q^{51} +(2.87270 + 2.17889i) q^{52} +5.06566i q^{53} +(-4.67748 + 2.26300i) q^{54} +(-7.49104 - 12.9749i) q^{55} +0.0284946 q^{56} +(-2.30750 + 2.61790i) q^{57} +(8.02391 + 2.15000i) q^{58} +(13.8214 + 3.70343i) q^{59} +(-5.84632 - 1.17819i) q^{60} -0.0214935 q^{61} +(0.721399 + 1.24950i) q^{62} +(0.0791403 - 0.0323159i) q^{63} -1.00000i q^{64} +(7.61257 + 9.80688i) q^{65} +(3.35025 - 6.75082i) q^{66} +(-0.668189 + 0.668189i) q^{67} -6.71041i q^{68} +(-0.506305 - 0.761877i) q^{69} +(0.0947706 + 0.0253937i) q^{70} +(-9.32969 + 2.49988i) q^{71} +(-1.13411 - 2.77737i) q^{72} +(6.53713 + 6.53713i) q^{73} -8.10826i q^{74} +(-10.6369 - 5.27880i) q^{75} +(-1.42466 - 1.42466i) q^{76} +(-0.0619924 + 0.107374i) q^{77} +(-1.98918 + 5.91973i) q^{78} +(1.40950 + 2.44132i) q^{79} +(0.891175 - 3.32591i) q^{80} +(-6.29967 - 6.42761i) q^{81} +(-4.35155 - 2.51237i) q^{82} +(-3.80210 + 14.1896i) q^{83} +(0.0157469 + 0.0467747i) q^{84} +(5.98015 - 22.3182i) q^{85} +(-2.26772 - 8.46324i) q^{86} +(0.904943 + 14.3596i) q^{87} +(3.76822 + 2.17558i) q^{88} +(10.8696 + 2.91249i) q^{89} +(-1.29681 - 10.2480i) q^{90} +(0.0387852 - 0.0951367i) q^{91} +(0.457384 - 0.264071i) q^{92} +(-1.65242 + 1.87470i) q^{93} +0.803143 q^{94} +(-3.46867 - 6.00791i) q^{95} +(1.64153 - 0.552626i) q^{96} +(0.333814 - 0.333814i) q^{97} +(1.81152 + 6.76070i) q^{98} +(12.9331 + 1.76884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.958654	−	1.44256i	−0.553479	−	0.832863i
$3$	−0.958654	−	1.44256i	−0.553479	−	0.832863i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	3.32591	−	0.891175i	1.48739	−	0.398545i	0.578536	−	0.815657i	$-0.303624\pi$
$5$	3.32591	−	0.891175i	1.48739	−	0.398545i	0.908855	+	0.417111i	$0.136957\pi$
$6$	1.29935	+	1.14529i	0.530458	+	0.467562i
$7$	−0.0201488	−	0.0201488i	−0.00761551	−	0.00761551i	0.703289	−	0.710904i	$-0.251714\pi$
$7$	−0.0201488	−	0.0201488i	−0.00761551	−	0.00761551i	−0.710904	+	0.703289i	$0.751714\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.16197	+	2.76583i	−0.387322	+	0.921945i
$10$	−2.98193	+	1.72162i	−0.942969	+	0.544423i
$11$	−1.12616	−	4.20290i	−0.339551	−	1.26722i	−0.898850	−	0.438256i	$-0.855596\pi$
$11$	−1.12616	−	4.20290i	−0.339551	−	1.26722i	0.559299	−	0.828966i	$-0.311070\pi$
$12$	−1.55150	−	0.769968i	−0.447879	−	0.222271i
$13$	1.39839	+	3.32333i	0.387843	+	0.921726i
$13$	1.39839	+	3.32333i	0.387843	+	0.921726i
$14$	0.0246771	+	0.0142473i	0.00659523	+	0.00380776i
$15$	−4.47397	−	3.94350i	−1.15517	−	1.01821i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.35521	−	5.81139i	0.813757	−	1.40947i	−0.0964602	−	0.995337i	$-0.530752\pi$
$17$	3.35521	−	5.81139i	0.813757	−	1.40947i	0.910217	−	0.414131i	$-0.135915\pi$
$18$	0.406522	−	2.97233i	0.0958182	−	0.700585i
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	0.879960	−	0.475048i	$-0.157569\pi$
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	−0.999592	+	0.0285767i	$0.990903\pi$
$20$	2.43473	−	2.43473i	0.544423	−	0.544423i
$21$	−0.00975013	+	0.0483815i	−0.00212765	+	0.0105577i
$22$	2.17558	+	3.76822i	0.463835	+	0.803387i
$23$	0.528142			0.110125			0.0550626	−	0.998483i	$-0.482464\pi$
$23$	0.528142			0.110125			0.0550626	+	0.998483i	$0.482464\pi$
$24$	1.69792	+	0.342174i	0.346586	+	0.0698460i
$25$	5.93735	−	3.42793i	1.18747	−	0.685587i
$26$	−2.21088	−	2.84816i	−0.433589	−	0.558570i
$27$	5.10381	−	0.975270i	0.982228	−	0.187691i
$28$	−0.0275237	−	0.00737496i	−0.00520149	−	0.00139374i
$29$	−7.19404	−	4.15348i	−1.33590	−	0.771282i	−0.349703	−	0.936861i	$-0.613718\pi$
$29$	−7.19404	−	4.15348i	−1.33590	−	0.771282i	−0.986197	+	0.165578i	$0.947051\pi$
$30$	5.34218	+	2.65118i	0.975343	+	0.484037i
$31$	−0.373424	−	1.39364i	−0.0670689	−	0.250305i	0.924249	−	0.381790i	$-0.124692\pi$
$31$	−0.373424	−	1.39364i	−0.0670689	−	0.250305i	−0.991318	+	0.131485i	$0.958025\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−4.98334	+	5.65369i	−0.867488	+	0.984180i
$34$	−1.73678	+	6.48176i	−0.297856	+	1.11161i
$35$	−0.0849690	−	0.0490569i	−0.0143624	−	0.00829212i
$36$	0.376625	+	2.97627i	0.0627708	+	0.496044i
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	0.547605	+	0.836737i	$0.315540\pi$
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	−0.892608	+	0.450833i	$0.851127\pi$
$38$	1.00739	+	1.74484i	0.163420	+	0.283051i
$39$	3.45354	−	5.20318i	0.553009	−	0.833176i
$40$	−1.72162	+	2.98193i	−0.272212	+	0.471484i
$41$	3.55302	+	3.55302i	0.554889	+	0.554889i	0.927848	−	0.372959i	$-0.121657\pi$
$41$	3.55302	+	3.55302i	0.554889	+	0.554889i	−0.372959	+	0.927848i	$0.621657\pi$
$42$	−0.00310415	−	0.0492564i	−0.000478980	−	0.00760043i
$43$			8.76179i			1.33616i	0.744089	+	0.668080i	$0.232884\pi$
$43$			8.76179i			1.33616i	−0.744089	+	0.668080i	$0.767116\pi$
$44$	−3.07674	−	3.07674i	−0.463835	−	0.463835i
$45$	−1.39975	+	10.2344i	−0.208663	+	1.52566i
$46$	−0.510146	+	0.136693i	−0.0752169	+	0.0201543i
$47$	−0.775777	−	0.207869i	−0.113159	−	0.0303208i	0.201795	−	0.979428i	$-0.435322\pi$
$47$	−0.775777	−	0.207869i	−0.113159	−	0.0303208i	−0.314954	+	0.949107i	$0.601989\pi$
$48$	−1.72862	+	0.108938i	−0.249505	+	0.0157238i
$49$		−	6.99919i		−	0.999884i
$50$	−4.84783	+	4.84783i	−0.685587	+	0.685587i
$51$	−11.5998	+	0.731018i	−1.62429	+	0.102363i
$52$	2.87270	+	2.17889i	0.398372	+	0.302158i
$53$			5.06566i			0.695822i	0.937527	+	0.347911i	$0.113109\pi$
$53$			5.06566i			0.695822i	−0.937527	+	0.347911i	$0.886891\pi$
$54$	−4.67748	+	2.26300i	−0.636525	+	0.307955i
$55$	−7.49104	−	12.9749i	−1.01009	−	1.74953i
$56$	0.0284946			0.00380776
$57$	−2.30750	+	2.61790i	−0.305636	+	0.346749i
$58$	8.02391	+	2.15000i	1.05359	+	0.282309i
$59$	13.8214	+	3.70343i	1.79939	+	0.482145i	0.993883	−	0.110440i	$-0.0352259\pi$
$59$	13.8214	+	3.70343i	1.79939	+	0.482145i	0.805508	+	0.592585i	$0.201893\pi$
$60$	−5.84632	−	1.17819i	−0.754757	−	0.152103i
$61$	−0.0214935			−0.00275196			−0.00137598	−	0.999999i	$-0.500438\pi$
$61$	−0.0214935			−0.00275196			−0.00137598	+	0.999999i	$0.500438\pi$
$62$	0.721399	+	1.24950i	0.0916178	+	0.158687i
$63$	0.0791403	−	0.0323159i	0.00997074	−	0.00407143i
$64$		−	1.00000i		−	0.125000i
$65$	7.61257	+	9.80688i	0.944223	+	1.21639i
$66$	3.35025	−	6.75082i	0.412388	−	0.830969i
$67$	−0.668189	+	0.668189i	−0.0816322	+	0.0816322i	−0.746744	−	0.665112i	$-0.768384\pi$
$67$	−0.668189	+	0.668189i	−0.0816322	+	0.0816322i	0.665112	+	0.746744i	$0.268384\pi$
$68$		−	6.71041i		−	0.813757i
$69$	−0.506305	−	0.761877i	−0.0609520	−	0.0917192i
$70$	0.0947706	+	0.0253937i	0.0113273	+	0.00303513i
$71$	−9.32969	+	2.49988i	−1.10723	+	0.296682i	−0.765706	−	0.643191i	$-0.777610\pi$
$71$	−9.32969	+	2.49988i	−1.10723	+	0.296682i	−0.341525	+	0.939873i	$0.610943\pi$
$72$	−1.13411	−	2.77737i	−0.133656	−	0.327317i
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	0.977242	−	0.212129i	$-0.0680396\pi$
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	−0.212129	+	0.977242i	$0.568040\pi$
$74$		−	8.10826i		−	0.942566i
$75$	−10.6369	−	5.27880i	−1.22824	−	0.609543i
$76$	−1.42466	−	1.42466i	−0.163420	−	0.163420i
$77$	−0.0619924	+	0.107374i	−0.00706469	+	0.0122364i
$78$	−1.98918	+	5.91973i	−0.225230	+	0.670277i
$79$	1.40950	+	2.44132i	0.158581	+	0.274670i	0.934357	−	0.356338i	$-0.115975\pi$
$79$	1.40950	+	2.44132i	0.158581	+	0.274670i	−0.775776	+	0.631008i	$0.782641\pi$
$80$	0.891175	−	3.32591i	0.0996364	−	0.371848i
$81$	−6.29967	−	6.42761i	−0.699963	−	0.714179i
$82$	−4.35155	−	2.51237i	−0.480548	−	0.277444i
$83$	−3.80210	+	14.1896i	−0.417335	+	1.55752i	0.362777	+	0.931876i	$0.381829\pi$
$83$	−3.80210	+	14.1896i	−0.417335	+	1.55752i	−0.780112	+	0.625640i	$0.784838\pi$
$84$	0.0157469	+	0.0467747i	0.00171813	+	0.00510353i
$85$	5.98015	−	22.3182i	0.648638	−	2.42075i
$86$	−2.26772	−	8.46324i	−0.244534	−	0.912615i
$87$	0.904943	+	14.3596i	0.0970201	+	1.53951i
$88$	3.76822	+	2.17558i	0.401693	+	0.231918i
$89$	10.8696	+	2.91249i	1.15217	+	0.308724i	0.783835	−	0.620969i	$-0.213261\pi$
$89$	10.8696	+	2.91249i	1.15217	+	0.308724i	0.368337	+	0.929692i	$0.379927\pi$
$90$	−1.29681	−	10.2480i	−0.136696	−	1.08023i
$91$	0.0387852	−	0.0951367i	0.00406579	−	0.00997303i
$92$	0.457384	−	0.264071i	0.0476856	−	0.0275313i
$93$	−1.65242	+	1.87470i	−0.171348	+	0.194398i
$94$	0.803143			0.0828379
$95$	−3.46867	−	6.00791i	−0.355878	−	0.616399i
$96$	1.64153	−	0.552626i	0.167537	−	0.0564022i
$97$	0.333814	−	0.333814i	0.0338937	−	0.0338937i	−0.689957	−	0.723851i	$-0.742371\pi$
$97$	0.333814	−	0.333814i	0.0338937	−	0.0338937i	0.723851	+	0.689957i	$0.242371\pi$
$98$	1.81152	+	6.76070i	0.182991	+	0.682933i
$99$	12.9331	+	1.76884i	1.29982	+	0.177776i
$100$	3.42793	−	5.93735i	0.342793	−	0.593735i
$101$	−2.74544	+	4.75523i	−0.273181	+	0.473163i	−0.969675	−	0.244400i	$-0.921409\pi$
$101$	−2.74544	+	4.75523i	−0.273181	+	0.473163i	0.696494	+	0.717563i	$0.254742\pi$
$102$	11.0153	−	3.70835i	1.09068	−	0.367181i
$103$	3.62390	+	2.09226i	0.357073	+	0.206156i	0.667796	−	0.744344i	$-0.267238\pi$
$103$	3.62390	+	2.09226i	0.357073	+	0.206156i	−0.310723	+	0.950501i	$0.600571\pi$
$104$	−3.33876	−	1.36114i	−0.327392	−	0.133471i
$105$	0.0106883	+	0.169602i	0.00104307	+	0.0165514i
$106$	−1.31109	−	4.89306i	−0.127344	−	0.475256i
$107$	−2.85234	+	1.64680i	−0.275746	+	0.159202i	−0.631496	−	0.775379i	$-0.717559\pi$
$107$	−2.85234	+	1.64680i	−0.275746	+	0.159202i	0.355750	+	0.934581i	$0.384226\pi$
$108$	3.93239	−	3.39651i	0.378395	−	0.326830i
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	−0.916823	−	0.399294i	$-0.869255\pi$
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	0.399294	+	0.916823i	$0.369255\pi$
$110$	10.5939	+	10.5939i	1.01009	+	1.01009i
$111$	13.3099	−	4.48084i	1.26332	−	0.425302i
$112$	−0.0275237	+	0.00737496i	−0.00260075	+	0.000696868i
$113$	0.503942	−	0.290951i	0.0474068	−	0.0273704i	−0.476109	−	0.879386i	$-0.657953\pi$
$113$	0.503942	−	0.290951i	0.0474068	−	0.0273704i	0.523516	+	0.852016i	$0.324620\pi$
$114$	1.55131	−	3.12592i	0.145294	−	0.292769i
$115$	1.75655	−	0.470666i	0.163799	−	0.0438899i
$116$	−8.30696			−0.771282
$117$	−10.8167	+	0.00610869i	−1.00000	+	0.000564749i
$118$	−14.3089			−1.31725
$119$	−0.184695	+	0.0494890i	−0.0169310	+	0.00453665i
$120$	5.95205	−	0.375099i	0.543345	−	0.0342417i
$121$	−6.86984	+	3.96631i	−0.624531	+	0.360573i
$122$	0.0207611	−	0.00556292i	0.00187962	−	0.000503644i
$123$	1.71933	−	8.53157i	0.155027	−	0.769266i
$124$	−1.02021	−	1.02021i	−0.0916178	−	0.0916178i
$125$	4.51854	−	4.51854i	0.404150	−	0.404150i
$126$	−0.0680796	+	0.0516978i	−0.00606502	+	0.00460561i
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	−0.0694101	−	0.997588i	$-0.522112\pi$
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	0.829232	+	0.558905i	$0.188778\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	12.6394	−	8.39952i	1.11284	−	0.739537i
$130$	−9.89139	−	7.50244i	−0.867532	−	0.658008i
$131$	−15.6965	−	9.06236i	−1.37141	−	0.791782i	−0.380301	−	0.924863i	$-0.624180\pi$
$131$	−15.6965	−	9.06236i	−1.37141	−	0.791782i	−0.991105	+	0.133081i	$0.957513\pi$
$132$	−1.48886	+	7.38791i	−0.129588	+	0.643035i
$133$	−0.0287051	+	0.0497187i	−0.00248905	+	0.00431116i
$134$	0.472481	−	0.818361i	0.0408161	−	0.0706956i
$135$	16.1057	−	7.79204i	1.38615	−	0.670632i
$136$	1.73678	+	6.48176i	0.148928	+	0.555806i
$137$	11.8200	−	11.8200i	1.00985	−	1.00985i	0.00990200	−	0.999951i	$-0.496848\pi$
$137$	11.8200	−	11.8200i	1.00985	−	1.00985i	0.999951	−	0.00990200i	$-0.00315196\pi$
$138$	0.686241	+	0.604875i	0.0584167	+	0.0514904i
$139$	−2.54241	−	4.40359i	−0.215645	−	0.373508i	0.737827	−	0.674990i	$-0.235852\pi$
$139$	−2.54241	−	4.40359i	−0.215645	−	0.373508i	−0.953472	+	0.301482i	$0.902519\pi$
$140$	−0.0981137			−0.00829212
$141$	0.443838	+	1.31838i	0.0373779	+	0.111028i
$142$	8.36477	−	4.82940i	0.701956	−	0.405275i
$143$	12.3928	−	9.61989i	1.03634	−	0.804456i
$144$	1.81430	+	2.38921i	0.151192	+	0.199101i
$145$	−27.6282	−	7.40295i	−2.29440	−	0.614782i
$146$	−8.00631	−	4.62245i	−0.662607	−	0.382557i
$147$	−10.0968	+	6.70980i	−0.832767	+	0.553415i
$148$	2.09857	+	7.83198i	0.172502	+	0.643785i
$149$	−1.36845	+	5.10712i	−0.112108	+	0.418392i	−0.999054	−	0.0434804i	$-0.986155\pi$
$149$	−1.36845	+	5.10712i	−0.112108	+	0.418392i	0.886947	+	0.461872i	$0.152822\pi$
$150$	11.6407	+	2.34590i	0.950457	+	0.191542i
$151$	−2.52008	+	9.40508i	−0.205082	+	0.765375i	0.784343	+	0.620327i	$0.213000\pi$
$151$	−2.52008	+	9.40508i	−0.205082	+	0.765375i	−0.989425	+	0.145047i	$0.953667\pi$
$152$	1.74484	+	1.00739i	0.141526	+	0.0817098i
$153$	12.1747	+	16.0326i	0.984266	+	1.29616i
$154$	0.0320896	−	0.119760i	0.00258586	−	0.00965055i
$155$	−2.48395	−	4.30232i	−0.199515	−	0.345571i
$156$	0.389261	−	6.23285i	0.0311659	−	0.499028i
$157$	4.81339	−	8.33703i	0.384150	−	0.665368i	−0.607501	−	0.794319i	$-0.707828\pi$
$157$	4.81339	−	8.33703i	0.384150	−	0.665368i	0.991651	+	0.128952i	$0.0411612\pi$
$158$	−1.99333	−	1.99333i	−0.158581	−	0.158581i
$159$	7.30753	−	4.85622i	0.579525	−	0.385123i
$160$			3.44323i			0.272212i
$161$	−0.0106414	−	0.0106414i	−0.000838659	−	0.000838659i
$162$	7.74860	+	4.57812i	0.608788	+	0.359691i
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.186142	−	0.982523i	$-0.440402\pi$
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.652465	+	0.757819i	$0.273735\pi$
$164$	4.85352	+	1.30050i	0.378996	+	0.101552i
$165$	−11.5357	+	23.2447i	−0.898054	+	1.80960i
$166$		−	14.6902i		−	1.14018i
$167$	−10.5531	+	10.5531i	−0.816620	+	0.816620i	−0.985617	−	0.168997i	$-0.945947\pi$
$167$	−10.5531	+	10.5531i	−0.816620	+	0.816620i	0.168997	+	0.985617i	$0.445947\pi$
$168$	−0.0273165	−	0.0411053i	−0.00210751	−	0.00317134i
$169$	−9.08903	+	9.29459i	−0.699156	+	0.714969i
$170$			23.1055i			1.77211i
$171$	5.98857	+	0.819050i	0.457957	+	0.0626343i
$172$	4.38090	+	7.58793i	0.334040	+	0.578574i
$173$	−19.0603			−1.44912			−0.724562	−	0.689210i	$-0.757958\pi$
$173$	−19.0603			−1.44912			−0.724562	+	0.689210i	$0.757958\pi$
$174$	−4.59064	−	13.6361i	−0.348016	−	1.03375i
$175$	−0.188699	−	0.0505617i	−0.0142643	−	0.00382211i
$176$	−4.20290	−	1.12616i	−0.316805	−	0.0848878i
$177$	−7.90750	−	23.4885i	−0.594364	−	1.76550i
$178$	−11.2530			−0.843449
$179$	−12.0533	−	20.8769i	−0.900906	−	1.56041i	−0.826320	−	0.563200i	$-0.809570\pi$
$179$	−12.0533	−	20.8769i	−0.900906	−	1.56041i	−0.0745856	−	0.997215i	$-0.523763\pi$
$180$	3.90499	+	9.56315i	0.291061	+	0.712795i
$181$		−	1.16505i		−	0.0865977i	−0.999062	−	0.0432988i	$-0.986213\pi$
$181$		−	1.16505i		−	0.0865977i	0.999062	−	0.0432988i	$-0.0137868\pi$
$182$	−0.0128404	+	0.101933i	−0.000951797	+	0.00755580i
$183$	0.0206048	+	0.0310057i	0.00152315	+	0.00229201i
$184$	−0.373453	+	0.373453i	−0.0275313	+	0.0275313i
$185$			27.9187i			2.05262i
$186$	1.11091	−	2.23850i	0.0814558	−	0.164135i
$187$	−28.2032	−	7.55702i	−2.06242	−	0.552624i
$188$	−0.775777	+	0.207869i	−0.0565793	+	0.0151604i
$189$	−0.122486	−	0.0831849i	−0.00890953	−	0.00605081i
$190$	4.90544	+	4.90544i	0.355878	+	0.355878i
$191$			11.5646i			0.836783i	0.908267	+	0.418392i	$0.137406\pi$
$191$			11.5646i			0.836783i	−0.908267	+	0.418392i	$0.862594\pi$
$192$	−1.44256	+	0.958654i	−0.104108	+	0.0691849i
$193$	−1.01826	−	1.01826i	−0.0732962	−	0.0732962i	0.669508	−	0.742805i	$-0.266505\pi$
$193$	−1.01826	−	1.01826i	−0.0732962	−	0.0732962i	−0.742805	+	0.669508i	$0.766505\pi$
$194$	−0.236042	+	0.408837i	−0.0169468	+	0.0293528i
$195$	6.84921	−	20.3830i	0.490482	−	1.45966i
$196$	−3.49959	−	6.06147i	−0.249971	−	0.432962i
$197$	−1.07594	+	4.01546i	−0.0766575	+	0.286090i	−0.993604	−	0.112920i	$-0.963980\pi$
$197$	−1.07594	+	4.01546i	−0.0766575	+	0.286090i	0.916947	+	0.399010i	$0.130646\pi$
$198$	−12.9502	+	1.63876i	−0.920331	+	0.116461i
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	0.561910	−	0.827198i	$-0.310067\pi$
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	−0.435419	+	0.900228i	$0.643400\pi$
$200$	−1.77443	+	6.62226i	−0.125471	+	0.468264i
$201$	1.60446	+	0.323341i	0.113170	+	0.0228068i
$202$	1.42114	−	5.30377i	0.0999912	−	0.373172i
$203$	0.0612635	+	0.228638i	0.00429985	+	0.0160473i
$204$	−9.68018	+	6.43296i	−0.677748	+	0.450397i
$205$	14.9834	+	8.65067i	1.04649	+	0.604189i
$206$	−4.04193	−	1.08303i	−0.281615	−	0.0754585i
$207$	−0.613682	+	1.46075i	−0.0426539	+	0.101529i
$208$	3.57728	+	0.450627i	0.248040	+	0.0312453i
$209$	−7.59210	+	4.38330i	−0.525157	+	0.303199i
$210$	−0.0542202	−	0.161056i	−0.00374155	−	0.0111139i
$211$	19.1496			1.31831			0.659157	−	0.752005i	$-0.270913\pi$
$211$	19.1496			1.31831			0.659157	+	0.752005i	$0.270913\pi$
$212$	2.53283	+	4.38699i	0.173956	+	0.301300i
$213$	12.5502	+	11.0621i	0.859924	+	0.757965i
$214$	2.32893	−	2.32893i	0.159202	−	0.159202i
$215$	7.80829	+	29.1409i	0.532521	+	1.98739i
$216$	−2.91932	+	4.29856i	−0.198634	+	0.292480i
$217$	−0.0205560	+	0.0356041i	−0.00139543	+	0.00241696i
$218$	3.82061	−	6.61749i	0.258764	−	0.448193i
$219$	3.16337	−	15.6971i	0.213760	−	1.06071i
$220$	−12.9749	−	7.49104i	−0.874765	−	0.505046i
$221$	24.0050	+	3.02389i	1.61475	+	0.203409i
$222$	−11.6967	+	7.77302i	−0.785029	+	0.521691i
$223$	6.83797	+	25.5197i	0.457905	+	1.70892i	0.679406	+	0.733763i	$0.262238\pi$
$223$	6.83797	+	25.5197i	0.457905	+	1.70892i	−0.221501	+	0.975160i	$0.571096\pi$
$224$	0.0246771	−	0.0142473i	0.00164881	−	0.000951939i
$225$	2.58209	+	20.4049i	0.172139	+	1.36032i
$226$	−0.411467	+	0.411467i	−0.0273704	+	0.0273704i
$227$	−3.63037	−	3.63037i	−0.240956	−	0.240956i	0.576289	−	0.817246i	$-0.304500\pi$
$227$	−3.63037	−	3.63037i	−0.240956	−	0.240956i	−0.817246	+	0.576289i	$0.804500\pi$
$228$	−0.689403	+	3.42091i	−0.0456569	+	0.226556i
$229$	−7.67020	+	2.05522i	−0.506861	+	0.135813i	−0.503182	−	0.864180i	$-0.667838\pi$
$229$	−7.67020	+	2.05522i	−0.506861	+	0.135813i	−0.00367870	+	0.999993i	$0.501171\pi$
$230$	−1.57488	+	0.909258i	−0.103845	+	0.0599547i
$231$	0.214323	−	0.0135066i	0.0141014	−	0.000888672i
$232$	8.02391	−	2.15000i	0.526795	−	0.141154i
$233$	−0.240333			−0.0157448			−0.00787238	−	0.999969i	$-0.502506\pi$
$233$	−0.240333			−0.0157448			−0.00787238	+	0.999969i	$0.502506\pi$
$234$	10.4465	−	2.80546i	0.682909	−	0.183398i
$235$	−2.76541			−0.180395
$236$	13.8214	−	3.70343i	0.899695	−	0.241073i
$237$	2.17054	−	4.37367i	0.140991	−	0.284100i
$238$	0.165593	−	0.0956054i	0.0107338	−	0.00619718i
$239$	−6.49603	+	1.74060i	−0.420193	+	0.112590i	−0.462719	−	0.886505i	$-0.653126\pi$
$239$	−6.49603	+	1.74060i	−0.420193	+	0.112590i	0.0425261	+	0.999095i	$0.486459\pi$
$240$	−5.65216	+	1.90282i	−0.364845	+	0.122827i
$241$	−18.3499	−	18.3499i	−1.18202	−	1.18202i	−0.979220	−	0.202800i	$-0.934996\pi$
$241$	−18.3499	−	18.3499i	−1.18202	−	1.18202i	−0.202800	−	0.979220i	$-0.565004\pi$
$242$	5.60920	−	5.60920i	0.360573	−	0.360573i
$243$	−3.23301	+	15.2495i	−0.207398	+	0.978257i
$244$	−0.0186139	+	0.0107467i	−0.00119163	+	0.000687990i
$245$	−6.23750	−	23.2787i	−0.398499	−	1.48722i
$246$	0.547384	+	8.68586i	0.0348999	+	0.553790i
$247$	5.73840	−	4.45442i	0.365125	−	0.283428i
$248$	1.24950	+	0.721399i	0.0793434	+	0.0458089i
$249$	24.1143	−	8.11819i	1.52818	−	0.514469i
$250$	−3.19509	+	5.53406i	−0.202075	+	0.350005i
$251$	10.2804	−	17.8061i	0.648892	−	1.12391i	−0.334496	−	0.942397i	$-0.608566\pi$
$251$	10.2804	−	17.8061i	0.648892	−	1.12391i	0.983388	−	0.181517i	$-0.0581007\pi$
$252$	0.0523795	−	0.0675565i	0.00329960	−	0.00425566i
$253$	−0.594774	−	2.21973i	−0.0373931	−	0.139553i
$254$	−6.99146	+	6.99146i	−0.438683	+	0.438683i
$255$	−37.9283	+	12.7687i	−2.37516	+	0.799608i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.4381			0.963002			0.481501	−	0.876446i	$-0.340092\pi$
$257$	15.4381			0.963002			0.481501	+	0.876446i	$0.340092\pi$
$258$	−10.0348	+	11.3846i	−0.624738	+	0.708777i
$259$	0.200088	−	0.115521i	0.0124329	−	0.00717813i
$260$	11.4961	+	4.68673i	0.712959	+	0.290658i
$261$	19.8471	−	15.0713i	1.22850	−	0.932891i
$262$	17.5071	+	4.69102i	1.08159	+	0.289812i
$263$	−10.9321	−	6.31167i	−0.674104	−	0.389194i	0.123526	−	0.992341i	$-0.460580\pi$
$263$	−10.9321	−	6.31167i	−0.674104	−	0.389194i	−0.797630	+	0.603147i	$0.793913\pi$
$264$	−0.474007	−	7.52151i	−0.0291731	−	0.462917i
$265$	4.51439	+	16.8479i	0.277317	+	1.03496i
$266$	0.0148589	−	0.0554540i	0.000911055	−	0.00340010i
$267$	−6.21871	−	18.4721i	−0.380579	−	1.13047i
$268$	−0.244574	+	0.912763i	−0.0149397	+	0.0557559i
$269$	−13.5676	−	7.83325i	−0.827230	−	0.477602i	0.0256732	−	0.999670i	$-0.491827\pi$
$269$	−13.5676	−	7.83325i	−0.827230	−	0.477602i	−0.852903	+	0.522069i	$0.825160\pi$
$270$	−13.5401	+	11.6950i	−0.824027	+	0.711734i
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	0.690537	+	0.723297i	$0.257374\pi$
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	−0.959671	+	0.281126i	$0.909292\pi$
$272$	−3.35521	−	5.81139i	−0.203439	−	0.352367i
$273$	−0.174422	+	0.0352531i	−0.0105565	+	0.00213362i
$274$	−8.35802	+	14.4765i	−0.504926	+	0.874558i
$275$	−21.0937	−	21.0937i	−1.27200	−	1.27200i
$276$	−0.819411	−	0.406652i	−0.0493228	−	0.0244776i
$277$		−	19.5532i		−	1.17484i	−0.809284	−	0.587418i	$-0.800144\pi$
$277$		−	19.5532i		−	1.17484i	0.809284	−	0.587418i	$-0.199856\pi$
$278$	3.59552	+	3.59552i	0.215645	+	0.215645i
$279$	4.28847	+	0.586530i	0.256744	+	0.0351146i
$280$	0.0947706	−	0.0253937i	0.00566363	−	0.00151756i
$281$	29.5609	+	7.92083i	1.76346	+	0.472517i	0.987413	−	0.158162i	$-0.0505568\pi$
$281$	29.5609	+	7.92083i	1.76346	+	0.472517i	0.776044	+	0.630679i	$0.217223\pi$
$282$	−0.769936	−	1.15858i	−0.0458490	−	0.0689926i
$283$			23.6188i			1.40399i	0.712182	+	0.701995i	$0.247707\pi$
$283$			23.6188i			1.40399i	−0.712182	+	0.701995i	$0.752293\pi$
$284$	−6.82981	+	6.82981i	−0.405275	+	0.405275i
$285$	−5.34153	+	10.7633i	−0.316405	+	0.637561i
$286$	−9.48072	+	12.4996i	−0.560607	+	0.739116i
$287$		−	0.143178i		−	0.00845153i
$288$	−2.37085	−	1.83822i	−0.139704	−	0.108318i
$289$	−14.0148	−	24.2744i	−0.824401	−	1.42790i
$290$	28.6028			1.67962
$291$	−0.801559	−	0.161535i	−0.0469882	−	0.00946935i
$292$	8.92988	+	2.39276i	0.522582	+	0.140025i
$293$	−21.3337	−	5.71634i	−1.24633	−	0.333952i	−0.425411	−	0.905000i	$-0.639870\pi$
$293$	−21.3337	−	5.71634i	−1.24633	−	0.333952i	−0.820917	+	0.571048i	$0.806537\pi$
$294$	8.01610	−	9.09440i	0.467508	−	0.530396i
$295$	49.2691			2.86856
$296$	−4.05413	−	7.02196i	−0.235642	−	0.408143i
$297$	−9.84668	−	20.3525i	−0.571363	−	1.18097i
$298$		−	5.28728i		−	0.306284i
$299$	0.738546	+	1.75519i	0.0427112	+	0.101505i
$300$	−11.8512	+	0.746864i	−0.684229	+	0.0431202i
$301$	0.176539	−	0.176539i	0.0101755	−	0.0101755i
$302$		−	9.73686i		−	0.560293i
$303$	9.49164	−	0.598164i	0.545280	−	0.0343636i
$304$	−1.94612	−	0.521462i	−0.111618	−	0.0299079i
$305$	−0.0714854	+	0.0191545i	−0.00409324	+	0.00109678i
$306$	−15.9094	−	12.3352i	−0.909479	−	0.705158i
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	0.787461	−	0.616364i	$-0.211395\pi$
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	−0.616364	+	0.787461i	$0.711395\pi$
$308$			0.123985i			0.00706469i
$309$	−0.455853	−	7.23345i	−0.0259326	−	0.411497i
$310$	3.51283	+	3.51283i	0.199515	+	0.199515i
$311$	15.1300	−	26.2059i	0.857943	−	1.48600i	−0.0159450	−	0.999873i	$-0.505076\pi$
$311$	15.1300	−	26.2059i	0.857943	−	1.48600i	0.873888	−	0.486128i	$-0.161591\pi$
$312$	1.23718	+	6.12122i	0.0700417	+	0.346546i
$313$	−16.7332	−	28.9828i	−0.945817	−	1.63820i	−0.754107	−	0.656751i	$-0.771930\pi$
$313$	−16.7332	−	28.9828i	−0.945817	−	1.63820i	−0.191710	−	0.981452i	$-0.561403\pi$
$314$	−2.49159	+	9.29875i	−0.140609	+	0.524759i
$315$	0.234414	−	0.178008i	0.0132077	−	0.0100296i
$316$	2.44132	+	1.40950i	0.137335	+	0.0792905i
$317$	2.88814	−	10.7787i	0.162214	−	0.605392i	−0.836165	−	0.548478i	$-0.815207\pi$
$317$	2.88814	−	10.7787i	0.162214	−	0.605392i	0.998379	−	0.0569135i	$-0.0181259\pi$
$318$	−5.80165	+	6.58207i	−0.325340	+	0.369104i
$319$	−9.35500	+	34.9133i	−0.523779	+	1.95477i
$320$	−0.891175	−	3.32591i	−0.0498182	−	0.185924i
$321$	5.11002	+	2.53597i	0.285213	+	0.141544i
$322$	0.0130330	+	0.00752460i	0.000726300	+	0.000419330i
$323$	−13.0593	−	3.49922i	−0.726638	−	0.194702i
$324$	−8.66948	−	2.41664i	−0.481638	−	0.134258i
$325$	19.6949	+	14.9382i	1.09247	+	0.828623i
$326$	−9.59929	+	5.54215i	−0.531655	+	0.306951i
$327$	12.9741	+	2.61463i	0.717472	+	0.144589i
$328$	−5.02473			−0.277444
$329$	0.0114426	+	0.0198192i	0.000630853	+	0.00109267i
$330$	5.12648	−	25.4383i	0.282203	−	1.40033i
$331$	2.92713	−	2.92713i	0.160890	−	0.160890i	−0.622071	−	0.782961i	$-0.713709\pi$
$331$	2.92713	−	2.92713i	0.160890	−	0.160890i	0.782961	+	0.622071i	$0.213709\pi$
$332$	3.80210	+	14.1896i	0.208668	+	0.778758i
$333$	−19.2235	−	14.9048i	−1.05344	−	0.816778i
$334$	7.46214	−	12.9248i	0.408310	−	0.707213i
$335$	−1.62686	+	2.81781i	−0.0888850	+	0.153953i
$336$	0.0370245	+	0.0326346i	0.00201985	+	0.00178036i
$337$	−14.3966	−	8.31187i	−0.784232	−	0.452777i	0.0536959	−	0.998557i	$-0.482900\pi$
$337$	−14.3966	−	8.31187i	−0.784232	−	0.452777i	−0.837928	+	0.545781i	$0.816233\pi$
$338$	6.37371	−	11.3303i	0.346684	−	0.616287i
$339$	−0.902820	−	0.448046i	−0.0490345	−	0.0243345i
$340$	−5.98015	−	22.3182i	−0.324319	−	1.21038i
$341$	−5.43678	+	3.13893i	−0.294418	+	0.169982i
$342$	−5.99650	+	0.758814i	−0.324254	+	0.0410320i
$343$	−0.282066	+	0.282066i	−0.0152301	+	0.0152301i
$344$	−6.19552	−	6.19552i	−0.334040	−	0.334040i
$345$	−2.36289	−	2.08273i	−0.127214	−	0.112130i
$346$	18.4108	−	4.93316i	0.989770	−	0.265208i
$347$	−17.6269	+	10.1769i	−0.946261	+	0.546324i	−0.891918	−	0.452198i	$-0.850640\pi$
$347$	−17.6269	+	10.1769i	−0.946261	+	0.546324i	−0.0543438	+	0.998522i	$0.517307\pi$
$348$	7.96350	+	11.9833i	0.426888	+	0.642372i
$349$	18.8920	−	5.06210i	1.01127	−	0.270968i	0.285108	−	0.958495i	$-0.407971\pi$
$349$	18.8920	−	5.06210i	1.01127	−	0.270968i	0.726158	+	0.687527i	$0.241304\pi$
$350$	0.195355			0.0104422
$351$	10.3782	+	15.5978i	0.553949	+	0.832550i
$352$	4.35116			0.231918
$353$	−9.77585	+	2.61943i	−0.520316	+	0.139418i	−0.509413	−	0.860522i	$-0.670137\pi$
$353$	−9.77585	+	2.61943i	−0.520316	+	0.139418i	−0.0109033	+	0.999941i	$0.503471\pi$
$354$	13.7173	+	20.6415i	0.729068	+	1.09709i
$355$	−28.8019	+	16.6288i	−1.52864	+	0.882564i
$356$	10.8696	−	2.91249i	0.576086	−	0.154362i
$357$	0.248450	+	0.218992i	0.0131494	+	0.0115903i
$358$	17.0459	+	17.0459i	0.900906	+	0.900906i
$359$	−1.10596	+	1.10596i	−0.0583705	+	0.0583705i	−0.735689	−	0.677319i	$-0.763142\pi$
$359$	−1.10596	+	1.10596i	−0.0583705	+	0.0583705i	0.677319	+	0.735689i	$0.263142\pi$
$360$	−6.24706	−	8.22661i	−0.329249	−	0.433580i
$361$	12.9390	−	7.47034i	0.681001	−	0.393176i
$362$	0.301538	+	1.12535i	0.0158485	+	0.0591473i
$363$	12.3074	+	6.10786i	0.645973	+	0.320579i
$364$	−0.0139794	−	0.101783i	−0.000732718	−	0.00533490i
$365$	27.5676	+	15.9162i	1.44296	+	0.833091i
$366$	−0.0279276	−	0.0246163i	−0.00145980	−	0.00128671i
$367$	3.11681	−	5.39847i	0.162696	−	0.281798i	−0.773139	−	0.634237i	$-0.781314\pi$
$367$	3.11681	−	5.39847i	0.162696	−	0.281798i	0.935835	+	0.352439i	$0.114648\pi$
$368$	0.264071	−	0.457384i	0.0137656	−	0.0238428i
$369$	−13.9556	+	5.69858i	−0.726498	+	0.296656i
$370$	−7.22588	−	26.9673i	−0.375656	−	1.40197i
$371$	0.102067	−	0.102067i	0.00529904	−	0.00529904i
$372$	−0.493689	+	2.44975i	−0.0255966	+	0.127014i
$373$	10.5545	+	18.2810i	0.546493	+	0.946554i	0.998511	+	0.0545455i	$0.0173710\pi$
$373$	10.5545	+	18.2810i	0.546493	+	0.946554i	−0.452018	+	0.892009i	$0.649296\pi$
$374$	29.1981			1.50980
$375$	−10.8500	−	2.18655i	−0.560291	−	0.112913i
$376$	0.695542	−	0.401572i	0.0358699	−	0.0207095i
$377$	3.74334	−	29.7163i	0.192792	−	1.53047i
$378$	0.139842	+	0.0486488i	0.00719270	+	0.00250222i
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	0.291769	−	0.956489i	$-0.405756\pi$
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	−0.225565	+	0.974228i	$0.572423\pi$
$380$	−6.00791	−	3.46867i	−0.308199	−	0.177939i
$381$	−15.3403	−	7.61299i	−0.785908	−	0.390025i
$382$	−2.99313	−	11.1705i	−0.153142	−	0.571534i
$383$	6.69236	−	24.9762i	0.341963	−	1.27622i	−0.554156	−	0.832413i	$-0.686959\pi$
$383$	6.69236	−	24.9762i	0.341963	−	1.27622i	0.896120	−	0.443812i	$-0.146374\pi$
$384$	1.14529	−	1.29935i	0.0584453	−	0.0663072i
$385$	−0.110492	+	0.412362i	−0.00563120	+	0.0210159i
$386$	1.24711	+	0.720021i	0.0634764	+	0.0366481i
$387$	−24.2337	−	10.1809i	−1.23187	−	0.517524i
$388$	0.122184	−	0.455998i	0.00620297	−	0.0231498i
$389$	7.30331	+	12.6497i	0.370292	+	0.641365i	0.989610	−	0.143775i	$-0.0459242\pi$
$389$	7.30331	+	12.6497i	0.370292	+	0.641365i	−0.619318	+	0.785140i	$0.712591\pi$
$390$	−1.34032	+	21.4612i	−0.0678697	+	1.08673i
$391$	1.77202	−	3.06924i	0.0896151	−	0.155218i
$392$	4.94917	+	4.94917i	0.249971	+	0.249971i
$393$	1.97447	+	31.3308i	0.0995988	+	1.58043i
$394$		−	4.15711i		−	0.209432i
$395$	6.86351	+	6.86351i	0.345341	+	0.345341i
$396$	12.0848	−	4.93468i	0.607284	−	0.247977i
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	−0.185772	−	0.982593i	$-0.559479\pi$
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	0.330413	+	0.943837i	$0.392812\pi$
$398$	−1.99021	−	0.533275i	−0.0997601	−	0.0267307i
$399$	0.0992406	−	0.00625415i	0.00496824	−	0.000313099i
$400$		−	6.85587i		−	0.342793i
$401$	−7.83107	+	7.83107i	−0.391065	+	0.391065i	−0.875067	−	0.484002i	$-0.839183\pi$
$401$	−7.83107	+	7.83107i	−0.391065	+	0.391065i	0.484002	+	0.875067i	$0.339183\pi$
$402$	−1.63348	+	0.102942i	−0.0814706	+	0.00513429i
$403$	4.10932	−	3.18985i	0.204700	−	0.158898i
$404$			5.49087i			0.273181i
$405$	−26.6803	−	15.7635i	−1.32575	−	0.783296i
$406$	−0.118352	−	0.204992i	−0.00587371	−	0.0101736i
$407$	35.2804			1.74878
$408$	7.68536	−	8.71918i	0.380482	−	0.431664i
$409$	−14.1786	−	3.79916i	−0.701089	−	0.187856i	−0.109371	−	0.994001i	$-0.534884\pi$
$409$	−14.1786	−	3.79916i	−0.701089	−	0.187856i	−0.591718	+	0.806145i	$0.701550\pi$
$410$	−16.7118	−	4.47792i	−0.825337	−	0.221148i
$411$	−28.3824	−	5.71980i	−1.40000	−	0.282137i
$412$	4.18452			0.206156
$413$	−0.203864	−	0.353103i	−0.0100315	−	0.0173751i
$414$	0.214701	−	1.56981i	0.0105520	−	0.0771520i
$415$			50.5818i			2.48296i
$416$	−3.57202	+	0.490596i	−0.175133	+	0.0240535i
$417$	−3.91515	+	7.88911i	−0.191726	+	0.386331i
$418$	6.19893	−	6.19893i	0.303199	−	0.303199i
$419$			28.1641i			1.37591i	0.725755	+	0.687953i	$0.241491\pi$
$419$			28.1641i			1.37591i	−0.725755	+	0.687953i	$0.758509\pi$
$420$	0.0940571	+	0.141535i	0.00458952	+	0.00690620i
$421$	7.03106	+	1.88397i	0.342673	+	0.0918189i	0.426051	−	0.904699i	$-0.359904\pi$
$421$	7.03106	+	1.88397i	0.342673	+	0.0918189i	−0.0833784	+	0.996518i	$0.526571\pi$
$422$	−18.4971	+	4.95629i	−0.900425	+	0.241268i
$423$	1.47636	−	1.90413i	0.0717829	−	0.0925821i
$424$	−3.58197	−	3.58197i	−0.173956	−	0.173956i
$425$		−	46.0057i		−	2.23160i
$426$	−14.9856	−	7.43697i	−0.726056	−	0.360322i
$427$	0.000433067	0	0.000433067i	2.09576e−5	0	2.09576e-5i
$428$	−1.64680	+	2.85234i	−0.0796011	+	0.137873i
$429$	−25.7577	−	8.65524i	−1.24359	−	0.417879i
$430$	−15.0845	−	26.1270i	−0.727437	−	1.25996i
$431$	−4.90556	+	18.3078i	−0.236292	+	0.881855i	0.741270	+	0.671207i	$0.234224\pi$
$431$	−4.90556	+	18.3078i	−0.236292	+	0.881855i	−0.977562	+	0.210648i	$0.932443\pi$
$432$	1.70729	−	4.90766i	0.0821423	−	0.236120i
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.982381	−	0.186890i	$-0.0598407\pi$
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.329339	+	0.944212i	$0.393174\pi$
$434$	0.0106406	−	0.0397112i	0.000510764	−	0.00190620i
$435$	15.8067	+	46.9522i	0.757872	+	2.25119i
$436$	−1.97769	+	7.38085i	−0.0947143	+	0.353479i
$437$	−0.275406	−	1.02783i	−0.0131744	−	0.0491677i
$438$	1.00712	+	15.9809i	0.0481220	+	0.763598i
$439$	11.1606	+	6.44360i	0.532668	+	0.307536i	0.742102	−	0.670287i	$-0.233829\pi$
$439$	11.1606	+	6.44360i	0.532668	+	0.307536i	−0.209434	+	0.977823i	$0.567162\pi$
$440$	14.4716	+	3.87765i	0.689905	+	0.184860i
$441$	19.3586	+	8.13282i	0.921838	+	0.387277i
$442$	−23.9697	+	3.29210i	−1.14012	+	0.156589i
$443$	−10.9018	+	6.29415i	−0.517959	+	0.299044i	−0.736099	−	0.676874i	$-0.763334\pi$
$443$	−10.9018	+	6.29415i	−0.517959	+	0.299044i	0.218140	+	0.975917i	$0.430001\pi$
$444$	9.28631	−	10.5355i	0.440709	−	0.499992i
$445$	38.7467			1.83677
$446$	−13.2099	−	22.8803i	−0.625509	−	1.08341i
$447$	8.67920	−	2.92189i	0.410512	−	0.138201i
$448$	−0.0201488	+	0.0201488i	−0.000951939	+	0.000951939i
$449$	−1.16977	−	4.36565i	−0.0552050	−	0.206028i	0.932814	−	0.360357i	$-0.117345\pi$
$449$	−1.16977	−	4.36565i	−0.0552050	−	0.206028i	−0.988020	+	0.154329i	$0.950678\pi$
$450$	−7.77528	−	19.0413i	−0.366530	−	0.897615i
$451$	10.9317	−	18.9343i	0.514754	−	0.891581i
$452$	0.290951	−	0.503942i	0.0136852	−	0.0237034i
$453$	15.9833	−	5.38084i	0.750961	−	0.252814i
$454$	4.44628	+	2.56706i	0.208674	+	0.120478i
$455$	0.0442127	−	0.350980i	0.00207272	−	0.0164542i
$456$	−0.219485	−	3.48278i	−0.0102783	−	0.163096i
$457$	2.63241	+	9.82430i	0.123139	+	0.459562i	0.999767	−	0.0216084i	$-0.00687869\pi$
$457$	2.63241	+	9.82430i	0.123139	+	0.459562i	−0.876627	+	0.481170i	$0.840212\pi$
$458$	6.87691	−	3.97039i	0.321337	−	0.185524i
$459$	11.4567	−	32.9324i	0.534751	−	1.53715i
$460$	1.28588	−	1.28588i	0.0599547	−	0.0599547i
$461$	−19.2384	−	19.2384i	−0.896021	−	0.896021i	0.0990604	−	0.995081i	$-0.468416\pi$
$461$	−19.2384	−	19.2384i	−0.896021	−	0.896021i	−0.995081	+	0.0990604i	$0.968416\pi$
$462$	−0.203524	+	0.0685172i	−0.00946880	+	0.00318771i
$463$	11.4472	−	3.06727i	0.531996	−	0.142548i	0.0171864	−	0.999852i	$-0.494529\pi$
$463$	11.4472	−	3.06727i	0.531996	−	0.142548i	0.514810	+	0.857304i	$0.327862\pi$
$464$	−7.19404	+	4.15348i	−0.333975	+	0.192821i
$465$	−3.82512	+	7.70769i	−0.177386	+	0.357435i
$466$	0.232144	−	0.0622029i	0.0107539	−	0.00288149i
$467$	−0.615879			−0.0284995			−0.0142497	−	0.999898i	$-0.504536\pi$
$467$	−0.615879			−0.0284995			−0.0142497	+	0.999898i	$0.504536\pi$
$468$	−9.36444	+	5.41362i	−0.432871	+	0.250245i
$469$	0.0269263			0.00124334
$470$	2.67118	−	0.715741i	0.123212	−	0.0330147i
$471$	−16.6410	+	1.04872i	−0.766779	+	0.0483225i
$472$	−12.3919	+	7.15447i	−0.570384	+	0.329311i
$473$	36.8249	−	9.86721i	1.69321	−	0.453695i
$474$	−0.964588	+	4.78642i	−0.0443050	+	0.219847i
$475$	−9.76728	−	9.76728i	−0.448153	−	0.448153i
$476$	−0.135206	+	0.135206i	−0.00619718	+	0.00619718i
$477$	−14.0108	−	5.88613i	−0.641510	−	0.269507i
$478$	5.82418	−	3.36259i	0.266392	−	0.153801i
$479$	5.18682	+	19.3575i	0.236992	+	0.884466i	0.977241	+	0.212133i	$0.0680410\pi$
$479$	5.18682	+	19.3575i	0.236992	+	0.884466i	−0.740249	+	0.672333i	$0.765292\pi$
$480$	4.96708	−	3.30087i	0.226715	−	0.150663i
$481$	−28.9629	+	3.97788i	−1.32059	+	0.181376i
$482$	22.4739	+	12.9753i	1.02366	+	0.591010i
$483$	−0.00514945	+	0.0255523i	−0.000234308	+	0.00116267i
$484$	−3.96631	+	6.86984i	−0.180287	+	0.312266i
$485$	0.812748	−	1.40772i	0.0369050	−	0.0639213i
$486$	−0.824012	−	15.5667i	−0.0373779	−	0.706118i
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	−0.971845	−	0.235620i	$-0.924288\pi$
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	0.723833	−	0.689975i	$-0.242379\pi$
$488$	0.0151982	−	0.0151982i	0.000687990	−	0.000687990i
$489$	−14.4024	−	12.6947i	−0.651299	−	0.574076i
$490$	12.0499	+	20.8711i	0.544360	+	0.942859i
$491$	−19.7513			−0.891362			−0.445681	−	0.895192i	$-0.647039\pi$
$491$	−19.7513			−0.891362			−0.445681	+	0.895192i	$0.647039\pi$
$492$	−2.77680	−	8.24823i	−0.125188	−	0.371859i
$493$	−48.2750	+	27.8716i	−2.17420	+	1.25527i
$494$	−4.38998	+	5.78784i	−0.197514	+	0.260407i
$495$	44.5906	−	5.64262i	2.00420	−	0.253617i
$496$	−1.39364	−	0.373424i	−0.0625761	−	0.0167672i
$497$	0.238351	+	0.137612i	0.0106915	+	0.00617275i
$498$	−21.1915	+	14.0828i	−0.949614	+	0.631066i
$499$	−1.37420	−	5.12859i	−0.0615177	−	0.229587i	0.928321	−	0.371778i	$-0.121252\pi$
$499$	−1.37420	−	5.12859i	−0.0615177	−	0.229587i	−0.989839	+	0.142191i	$0.954585\pi$
$500$	1.65390	−	6.17244i	0.0739647	−	0.276040i
$501$	25.3402	+	5.10670i	1.13211	+	0.228151i
$502$	−5.32152	+	19.8602i	−0.237511	+	0.886403i
$503$	−16.2322	−	9.37164i	−0.723756	−	0.417861i	0.0923776	−	0.995724i	$-0.470553\pi$
$503$	−16.2322	−	9.37164i	−0.723756	−	0.417861i	−0.816134	+	0.577863i	$0.803887\pi$
$504$	−0.0331098	+	0.0788114i	−0.00147483	+	0.00351054i
$505$	−4.89333	+	18.2621i	−0.217750	+	0.812654i
$506$	1.14901	+	1.99015i	0.0510799	+	0.0884731i
$507$	22.1213	+	4.20119i	0.982440	+	0.186581i
$508$	4.94371	−	8.56275i	0.219342	−	0.379911i
$509$	−12.0815	−	12.0815i	−0.535502	−	0.535502i	0.386703	−	0.922204i	$-0.373614\pi$
$509$	−12.0815	−	12.0815i	−0.535502	−	0.535502i	−0.922204	+	0.386703i	$0.873614\pi$
$510$	33.3311	−	22.1502i	1.47593	−	0.980827i
$511$		−	0.263430i		−	0.0116535i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.55943	−	9.42406i	−0.201304	−	0.416083i
$514$	−14.9121	+	3.99567i	−0.657743	+	0.176242i
$515$	13.9173	+	3.72914i	0.613271	+	0.164325i
$516$	6.74630	−	13.5939i	0.296989	−	0.598439i
$517$			3.49461i			0.153693i
$518$	−0.163371	+	0.163371i	−0.00717813	+	0.00717813i
$519$	18.2722	+	27.4956i	0.802060	+	1.20692i
$520$	−12.3174	−	1.55161i	−0.540154	−	0.0680427i
$521$		−	6.18564i		−	0.270998i	−0.990777	−	0.135499i	$-0.956736\pi$
$521$		−	6.18564i		−	0.270998i	0.990777	−	0.135499i	$-0.0432637\pi$
$522$	−15.2701	+	19.6946i	−0.668352	+	0.862008i
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	0.929453	−	0.368941i	$-0.120280\pi$
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	−0.784239	+	0.620459i	$0.786946\pi$
$524$	−18.1247			−0.791782
$525$	0.107959	+	0.320681i	0.00471170	+	0.0139957i
$526$	12.1932	+	3.26716i	0.531649	+	0.142455i
$527$	−9.35188	−	2.50583i	−0.407374	−	0.109156i
$528$	2.40457	+	7.14254i	0.104645	+	0.310839i
$529$	−22.7211			−0.987872
$530$	−8.72113	−	15.1054i	−0.378822	−	0.656139i
$531$	−26.3030	+	33.9244i	−1.14145	+	1.47219i
$532$			0.0574102i			0.00248905i
$533$	−6.83937	+	16.7764i	−0.296246	+	0.726665i
$534$	10.7877	+	16.2332i	0.466831	+	0.702477i
$535$	−8.01904	+	8.01904i	−0.346693	+	0.346693i
$536$		−	0.944962i		−	0.0408161i
$537$	−18.5613	+	37.4014i	−0.800979	+	1.61399i
$538$	15.1327	+	4.05479i	0.652416	+	0.174814i
$539$	−29.4169	+	7.88223i	−1.26708	+	0.339512i
$540$	10.0519	−	14.8009i	0.432565	−	0.636931i
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	0.794273	−	0.607561i	$-0.207852\pi$
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	−0.607561	+	0.794273i	$0.707852\pi$
$542$		−	17.1182i		−	0.735289i
$543$	−1.68066	+	1.11688i	−0.0721240	+	0.0479300i
$544$	4.74498	+	4.74498i	0.203439	+	0.203439i
$545$	−13.1553	+	22.7856i	−0.563509	+	0.976027i
$546$	0.159355	−	0.0791956i	0.00681975	−	0.00338926i
$547$	−16.4189	−	28.4384i	−0.702022	−	1.21594i	−0.967755	−	0.251892i	$-0.918947\pi$
$547$	−16.4189	−	28.4384i	−0.702022	−	1.21594i	0.265733	−	0.964047i	$-0.414386\pi$
$548$	4.32643	−	16.1465i	0.184816	−	0.689742i
$549$	0.0249747	−	0.0594474i	0.00106589	−	0.00253715i
$550$	25.8344	+	14.9155i	1.10158	+	0.635999i
$551$	−4.33176	+	16.1664i	−0.184539	+	0.688710i
$552$	0.896740	+	0.180716i	0.0381678	+	0.00769180i
$553$	0.0207900	−	0.0775892i	0.000884079	−	0.00329943i
$554$	5.06073	+	18.8869i	0.215010	+	0.802428i
$555$	40.2744	−	26.7643i	1.70955	−	1.13608i
$556$	−4.40359	−	2.54241i	−0.186754	−	0.107822i
$557$	−7.73861	−	2.07355i	−0.327895	−	0.0878593i	0.0911160	−	0.995840i	$-0.470957\pi$
$557$	−7.73861	−	2.07355i	−0.327895	−	0.0878593i	−0.419011	+	0.907981i	$0.637623\pi$
$558$	−4.29415	+	0.543394i	−0.181786	+	0.0230037i
$559$	−29.1183	+	12.2524i	−1.23157	+	0.518220i
$560$	−0.0849690	+	0.0490569i	−0.00359059	+	0.00207303i
$561$	16.1356	+	47.9294i	0.681247	+	2.02358i
$562$	−30.6037			−1.29094
$563$	7.44232	+	12.8905i	0.313656	+	0.543269i	0.979151	−	0.203134i	$-0.0651127\pi$
$563$	7.44232	+	12.8905i	0.313656	+	0.543269i	−0.665495	+	0.746403i	$0.731779\pi$
$564$	1.04356	+	0.919831i	0.0439420	+	0.0387319i
$565$	1.41678	−	1.41678i	0.0596042	−	0.0596042i
$566$	−6.11299	−	22.8140i	−0.256948	−	0.958943i
$567$	−0.00257777	+	0.256439i	−0.000108256	+	0.0107694i
$568$	4.82940	−	8.36477i	0.202637	−	0.350978i
$569$	−4.45227	+	7.71156i	−0.186649	+	0.323285i	−0.944131	−	0.329571i	$-0.893096\pi$
$569$	−4.45227	+	7.71156i	−0.186649	+	0.323285i	0.757482	+	0.652856i	$0.226429\pi$
$570$	2.37378	−	11.7790i	0.0994266	−	0.493369i
$571$	0.862884	+	0.498186i	0.0361106	+	0.0208484i	0.517947	−	0.855413i	$-0.326697\pi$
$571$	0.862884	+	0.498186i	0.0361106	+	0.0208484i	−0.481836	+	0.876261i	$0.660030\pi$
$572$	5.92254	−	14.5275i	0.247634	−	0.607424i
$573$	16.6826	−	11.0864i	0.696926	−	0.463142i
$574$	0.0370572	+	0.138299i	0.00154674	+	0.00577250i
$575$	3.13576	−	1.81043i	0.130770	−	0.0755003i
$576$	2.76583	+	1.16197i	0.115243	+	0.0484152i
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	−0.948247	−	0.317534i	$-0.897145\pi$
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	0.317534	+	0.948247i	$0.397145\pi$
$578$	19.8199	+	19.8199i	0.824401	+	0.824401i
$579$	−0.492745	+	2.44507i	−0.0204778	+	0.101614i
$580$	−27.6282	+	7.40295i	−1.14720	+	0.307391i
$581$	0.362511	−	0.209296i	0.0150395	−	0.00868306i
$582$	0.816055	−	0.0514279i	0.0338266	−	0.00213175i
$583$	21.2905	−	5.70477i	0.881762	−	0.236267i
$584$	−9.24490			−0.382557
$585$	−35.9698	+	9.65984i	−1.48717	+	0.399385i
$586$	22.0863			0.912375
$587$	−6.18262	+	1.65663i	−0.255184	+	0.0683763i	−0.384143	−	0.923274i	$-0.625503\pi$
$587$	−6.18262	+	1.65663i	−0.255184	+	0.0683763i	0.128959	+	0.991650i	$0.458836\pi$
$588$	−5.38915	+	10.8592i	−0.222245	+	0.447827i
$589$	−2.51746	+	1.45346i	−0.103730	+	0.0598886i
$590$	−47.5903	+	12.7518i	−1.95926	+	0.524982i
$591$	6.82400	−	2.29733i	0.280702	−	0.0944995i
$592$	5.73341	+	5.73341i	0.235642	+	0.235642i
$593$	24.4287	−	24.4287i	1.00317	−	1.00317i	0.00317304	−	0.999995i	$-0.498990\pi$
$593$	24.4287	−	24.4287i	1.00317	−	1.00317i	0.999995	−	0.00317304i	$-0.00101001\pi$
$594$	14.7788	+	17.1105i	0.606381	+	0.702051i
$595$	−0.570177	+	0.329192i	−0.0233750	+	0.0134955i
$596$	1.36845	+	5.10712i	0.0560538	+	0.209196i
$597$	−0.224457	−	3.56168i	−0.00918643	−	0.145770i
$598$	−1.16766	−	1.50423i	−0.0477490	−	0.0615126i
$599$	36.9806	+	21.3507i	1.51099	+	0.872368i	0.999918	+	0.0128274i	$0.00408321\pi$
$599$	36.9806	+	21.3507i	1.51099	+	0.872368i	0.511068	+	0.859540i	$0.329250\pi$
$600$	11.2541	−	3.78873i	0.459446	−	0.154674i
$601$	13.5165	−	23.4112i	0.551349	−	0.954965i	−0.446829	−	0.894620i	$-0.647447\pi$
$601$	13.5165	−	23.4112i	0.551349	−	0.954965i	0.998178	−	0.0603449i	$-0.0192201\pi$
$602$	−0.124832	+	0.216215i	−0.00508777	+	0.00881228i
$603$	−1.07169	−	2.62451i	−0.0436424	−	0.106878i
$604$	2.52008	+	9.40508i	0.102541	+	0.382687i
$605$	−19.3138	+	19.3138i	−0.785218	+	0.785218i
$606$	−9.01340	+	3.03440i	−0.366144	+	0.123264i
$607$	−23.5378	−	40.7687i	−0.955370	−	1.65475i	−0.733519	−	0.679669i	$-0.762124\pi$
$607$	−23.5378	−	40.7687i	−0.955370	−	1.65475i	−0.221851	−	0.975081i	$-0.571210\pi$
$608$	2.01477			0.0817098
$609$	0.271094	−	0.307561i	0.0109853	−	0.0124630i
$610$	0.0640921	−	0.0370036i	0.00259501	−	0.00149823i
$611$	−0.394019	−	2.86884i	−0.0159403	−	0.116061i
$612$	18.5599	+	7.79727i	0.750239	+	0.315186i
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.687217	−	0.726452i	$-0.258832\pi$
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.231922	+	0.972734i	$0.425499\pi$
$614$	−3.67161	−	2.11981i	−0.148174	−	0.0855484i
$615$	−1.88477	−	29.9075i	−0.0760013	−	1.20599i
$616$	−0.0320896	−	0.119760i	−0.00129293	−	0.00482527i
$617$	1.25606	−	4.68769i	0.0505672	−	0.188719i	−0.936022	−	0.351941i	$-0.885522\pi$
$617$	1.25606	−	4.68769i	0.0505672	−	0.188719i	0.986589	+	0.163222i	$0.0521885\pi$
$618$	2.31247	+	6.86899i	0.0930214	+	0.276311i
$619$	−6.61442	+	24.6854i	−0.265856	+	0.992188i	0.695868	+	0.718170i	$0.255020\pi$
$619$	−6.61442	+	24.6854i	−0.265856	+	0.992188i	−0.961724	+	0.274019i	$0.911647\pi$
$620$	−4.30232	−	2.48395i	−0.172785	−	0.0997577i
$621$	2.69553	−	0.515081i	0.108168	−	0.0206695i
$622$	−7.83186	+	29.2289i	−0.314029	+	1.17197i
$623$	−0.160325	−	0.277691i	−0.00642329	−	0.0111255i
$624$	−2.77932	−	5.59244i	−0.111262	−	0.223877i
$625$	−6.13822	+	10.6317i	−0.245529	+	0.425268i
$626$	23.6643	+	23.6643i	0.945817	+	0.945817i
$627$	13.6014	+	6.75000i	0.543187	+	0.269569i
$628$		−	9.62677i		−	0.384150i
$629$	38.4735	+	38.4735i	1.53404	+	1.53404i
$630$	−0.180355	+	0.232613i	−0.00718551	+	0.00926753i
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.136440	−	0.990648i	$-0.456434\pi$
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.613484	+	0.789707i	$0.289767\pi$
$632$	−2.72294	−	0.729610i	−0.108313	−	0.0290223i
$633$	−18.3579	−	27.6245i	−0.729659	−	1.09798i
$634$			11.1589i			0.443177i
$635$	24.0732	−	24.0732i	0.955317	−	0.955317i
$636$	3.90040	−	7.85937i	0.154661	−	0.311644i
$637$	23.2606	−	9.78757i	0.921619	−	0.387798i
$638$		−	36.1449i		−	1.43099i
$639$	3.92652	−	28.7092i	0.155331	−	1.13572i
$640$	1.72162	+	2.98193i	0.0680529	+	0.117871i
$641$	−22.8781			−0.903629			−0.451814	−	0.892112i	$-0.649223\pi$
$641$	−22.8781			−0.903629			−0.451814	+	0.892112i	$0.649223\pi$
$642$	−5.59225	−	1.12699i	−0.220709	−	0.0444786i
$643$	−12.7791	−	3.42415i	−0.503959	−	0.135035i	−0.00212223	−	0.999998i	$-0.500676\pi$
$643$	−12.7791	−	3.42415i	−0.503959	−	0.135035i	−0.501837	+	0.864962i	$0.667342\pi$
$644$	−0.0145364	−	0.00389502i	−0.000572815	−	0.000153485i
$645$	34.5521	−	39.2000i	1.36049	−	1.54350i
$646$	13.5200			0.531936
$647$	5.87399	+	10.1741i	0.230930	+	0.399983i	0.958082	−	0.286493i	$-0.0924897\pi$
$647$	5.87399	+	10.1741i	0.230930	+	0.399983i	−0.727152	+	0.686477i	$0.759156\pi$
$648$	8.99955	+	0.0904650i	0.353536	+	0.00355380i
$649$		−	62.2606i		−	2.44394i
$650$	−22.8901	−	9.33179i	−0.897822	−	0.366023i
$651$	0.0710671	−	0.00447866i	0.00278534	−	0.000175533i
$652$	7.83779	−	7.83779i	0.306951	−	0.306951i
$653$		−	9.22206i		−	0.360887i	−0.983585	−	0.180444i	$-0.942247\pi$
$653$		−	9.22206i		−	0.360887i	0.983585	−	0.180444i	$-0.0577533\pi$
$654$	−13.2088	+	0.832419i	−0.516504	+	0.0325501i
$655$	−60.2811	−	16.1523i	−2.35538	−	0.631122i
$656$	4.85352	−	1.30050i	0.189498	−	0.0507759i
$657$	−25.6765	+	10.4847i	−1.00174	+	0.409047i
$658$	−0.0161823	−	0.0161823i	−0.000630853	−	0.000630853i
$659$		−	4.26895i		−	0.166295i	−0.996537	−	0.0831474i	$-0.973503\pi$
$659$		−	4.26895i		−	0.166295i	0.996537	−	0.0831474i	$-0.0264972\pi$
$660$	1.63212	+	25.8983i	0.0635300	+	1.00809i
$661$	−31.5763	−	31.5763i	−1.22818	−	1.22818i	−0.964654	−	0.263522i	$-0.915116\pi$
$661$	−31.5763	−	31.5763i	−1.22818	−	1.22818i	−0.263522	−	0.964654i	$-0.584884\pi$
$662$	−2.06979	+	3.58499i	−0.0804448	+	0.139335i
$663$	−18.6504	−	37.5276i	−0.724320	−	1.45745i
$664$	−7.34510	−	12.7221i	−0.285045	−	0.493713i
$665$	−0.0511626	+	0.190941i	−0.00198400	+	0.00740438i
$666$	22.4261	+	9.42152i	0.868994	+	0.365077i
$667$	−3.79947	−	2.19363i	−0.147116	−	0.0849375i
$668$	−3.86269	+	14.4157i	−0.149452	+	0.557762i
$669$	30.2584	−	34.3287i	1.16986	−	1.32722i
$670$	0.842126	−	3.14286i	0.0325342	−	0.121419i
$671$	0.0242052	+	0.0903350i	0.000934431	+	0.00348734i
$672$	−0.0442094	−	0.0219400i	−0.00170541	−	0.000846352i
$673$	−4.88433	−	2.81997i	−0.188277	−	0.108702i	0.402899	−	0.915245i	$-0.368003\pi$
$673$	−4.88433	−	2.81997i	−0.188277	−	0.108702i	−0.591176	+	0.806543i	$0.701336\pi$
$674$	16.0573	+	4.30254i	0.618504	+	0.165728i
$675$	26.9599	−	23.2860i	1.03769	−	0.896280i
$676$	−3.22404	+	12.5939i	−0.124001	+	0.484380i
$677$	−21.2676	+	12.2789i	−0.817381	+	0.471915i	−0.849512	−	0.527569i	$-0.823104\pi$
$677$	−21.2676	+	12.2789i	−0.817381	+	0.471915i	0.0321318	+	0.999484i	$0.489770\pi$
$678$	0.988020	+	0.199112i	0.0379447	+	0.00764684i
$679$	−0.0134519			−0.000516235
$680$	11.5528	+	20.0100i	0.443028	+	0.767347i
$681$	−1.75676	+	8.71731i	−0.0673194	+	0.334048i
$682$	4.43911	−	4.43911i	0.169982	−	0.169982i
$683$	7.16139	+	26.7267i	0.274023	+	1.02267i	0.956493	+	0.291755i	$0.0942391\pi$
$683$	7.16139	+	26.7267i	0.274023	+	1.02267i	−0.682470	+	0.730913i	$0.739094\pi$
$684$	5.59578	−	2.28497i	0.213960	−	0.0873679i
$685$	28.7786	−	49.8460i	1.09957	−	1.90452i
$686$	0.199451	−	0.345459i	0.00761507	−	0.0131897i
$687$	10.3179	+	9.09449i	0.393651	+	0.346976i
$688$	7.58793	+	4.38090i	0.289287	+	0.167020i
$689$	−16.8349	+	7.08375i	−0.641357	+	0.269870i
$690$	2.82143	+	1.40020i	0.107410	+	0.0533046i
$691$	−2.04478	−	7.63123i	−0.0777871	−	0.290306i	0.916064	−	0.401033i	$-0.131349\pi$
$691$	−2.04478	−	7.63123i	−0.0777871	−	0.290306i	−0.993851	+	0.110727i	$0.964682\pi$
$692$	−16.5067	+	9.53013i	−0.627489	+	0.362281i
$693$	−0.224946	−	0.296226i	−0.00854497	−	0.0112527i
$694$	14.3923	−	14.3923i	0.546324	−	0.546324i
$695$	−12.3802	−	12.3802i	−0.469608	−	0.469608i
$696$	−10.7937	−	9.51387i	−0.409133	−	0.360622i
$697$	32.5691	−	8.72687i	1.23364	−	0.330554i
$698$	−16.9381	+	9.77922i	−0.641117	+	0.370149i
$699$	0.230397	+	0.346696i	0.00871440	+	0.0131132i
$700$	−0.188699	+	0.0505617i	−0.00713215	+	0.00191105i
$701$	39.9569			1.50915			0.754575	−	0.656214i	$-0.227843\pi$
$701$	39.9569			1.50915			0.754575	+	0.656214i	$0.227843\pi$
$702$	−14.0616	−	12.3803i	−0.530722	−	0.467263i
$703$	16.3363			0.616136
$704$	−4.20290	+	1.12616i	−0.158403	+	0.0424439i
$705$	2.65107	+	3.98927i	0.0998451	+	0.150245i
$706$	8.76479	−	5.06035i	0.329867	−	0.190449i
$707$	0.151129	−	0.0404949i	0.00568380	−	0.00152297i
$708$	−18.5923	−	16.3879i	−0.698743	−	0.615894i
$709$	−35.9885	−	35.9885i	−1.35158	−	1.35158i	−0.883898	−	0.467680i	$-0.845090\pi$
$709$	−35.9885	−	35.9885i	−1.35158	−	1.35158i	−0.467680	−	0.883898i	$-0.654910\pi$
$710$	23.5166	−	23.5166i	0.882564	−	0.882564i
$711$	−8.39008	+	1.06170i	−0.314653	+	0.0398170i
$712$	−9.74539	+	5.62650i	−0.365224	+	0.210862i
$713$	−0.197221	−	0.736038i	−0.00738597	−	0.0275648i
$714$	−0.296663	−	0.147226i	−0.0111023	−	0.00550980i
$715$	32.6444	−	43.0390i	1.22083	−	1.60957i
$716$	−20.8769	−	12.0533i	−0.780207	−	0.450453i
$717$	8.73837	+	7.70228i	0.326340	+	0.287647i
$718$	0.782034	−	1.35452i	0.0291853	−	0.0505504i
$719$	−0.750575	+	1.30003i	−0.0279917	+	0.0484831i	−0.879682	−	0.475563i	$-0.842245\pi$
$719$	−0.750575	+	1.30003i	−0.0279917	+	0.0484831i	0.851690	+	0.524046i	$0.175578\pi$
$720$	8.16340	+	6.32943i	0.304232	+	0.235884i
$721$	−0.0308606	−	0.115173i	−0.00114931	−	0.00428928i
$722$	−10.5647	+	10.5647i	−0.393176	+	0.393176i
$723$	−8.87965	+	44.0620i	−0.330238	+	1.63868i
$724$	−0.582526	−	1.00897i	−0.0216494	−	0.0374979i
$725$	−56.9514			−2.11512
$726$	−13.4689	−	2.71434i	−0.499878	−	0.100738i
$727$	41.9032	−	24.1928i	1.55410	−	0.897261i	0.556301	−	0.830981i	$-0.312220\pi$
$727$	41.9032	−	24.1928i	1.55410	−	0.897261i	0.997801	−	0.0662809i	$-0.0211133\pi$
$728$	0.0398465	+	0.0946971i	0.00147681	+	0.00350971i
$729$	25.0977	−	9.95518i	0.929544	−	0.368710i
$730$	−30.7477	−	8.23882i	−1.13802	−	0.304932i
$731$	50.9182	+	29.3976i	1.88328	+	1.08731i
$732$	0.0333471	+	0.0165493i	0.00123255	+	0.000611680i
$733$	−6.15729	−	22.9793i	−0.227425	−	0.848761i	−0.981419	−	0.191879i	$-0.938542\pi$
$733$	−6.15729	−	22.9793i	−0.227425	−	0.848761i	0.753994	−	0.656882i	$-0.228125\pi$
$734$	−1.61338	+	6.02121i	−0.0595509	+	0.222247i
$735$	−27.6013	+	31.3142i	−1.01809	+	1.15504i
$736$	−0.136693	+	0.510146i	−0.00503857	+	0.0188042i
$737$	3.56082	+	2.05584i	0.131164	+	0.0757279i
$738$	12.0051	−	9.11637i	0.441915	−	0.335578i
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	−0.282786	−	0.959183i	$-0.591259\pi$
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	0.724491	−	0.689284i	$-0.242075\pi$
$740$	13.9593	+	24.1783i	0.513155	+	0.888811i
$741$	−11.9269	−	4.00774i	−0.438146	−	0.147228i
$742$	−0.0721721	+	0.125006i	−0.00264952	+	0.00458911i
$743$	−25.5083	−	25.5083i	−0.935809	−	0.935809i	0.0622513	−	0.998061i	$-0.480172\pi$
$743$	−25.5083	−	25.5083i	−0.935809	−	0.935809i	−0.998061	+	0.0622513i	$0.980172\pi$
$744$	−0.157176	−	2.49405i	−0.00576233	−	0.0914364i
$745$			18.2053i			0.666992i
$746$	−14.9264	−	14.9264i	−0.546493	−	0.546493i
$747$	−34.8283	−	27.0039i	−1.27430	−	0.988020i
$748$	−28.2032	+	7.55702i	−1.03121	+	0.276312i
$749$	0.0906521	+	0.0242902i	0.00331236	+	0.000887543i
$750$	11.0462	−	0.696133i	0.403350	−	0.0254192i
$751$			17.5054i			0.638780i	0.947623	+	0.319390i	$0.103478\pi$
$751$			17.5054i			0.638780i	−0.947623	+	0.319390i	$0.896522\pi$
$752$	−0.567908	+	0.567908i	−0.0207095	+	0.0207095i
$753$	−35.5418	+	2.23985i	−1.29521	+	0.0816246i
$754$	4.07537	+	29.6726i	0.148416	+	1.08061i
$755$			33.5263i			1.22015i
$756$	−0.147668	−	0.0107973i	−0.00537064	−	0.000392694i
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	0.880484	−	0.474076i	$-0.157218\pi$
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	−0.850804	+	0.525483i	$0.823885\pi$
$758$	−1.33432			−0.0484645
$759$	−2.63191	+	2.98595i	−0.0955322	+	0.108383i
$760$	6.70095	+	1.79552i	0.243069	+	0.0651302i
$761$	17.1049	+	4.58324i	0.620051	+	0.166142i	0.555151	−	0.831750i	$-0.312660\pi$
$761$	17.1049	+	4.58324i	0.620051	+	0.166142i	0.0649002	+	0.997892i	$0.479327\pi$
$762$	16.7880	+	3.38322i	0.608165	+	0.122561i
$763$	0.217734			0.00788249
$764$	5.78229	+	10.0152i	0.209196	+	0.362338i
$765$	54.7798	+	42.4731i	1.98057	+	1.53562i
$766$			25.8573i			0.934261i
$767$	7.01992	+	51.1118i	0.253475	+	1.84554i
$768$	−0.769968	+	1.55150i	−0.0277838	+	0.0559849i
$769$	14.4842	−	14.4842i	0.522312	−	0.522312i	−0.395957	−	0.918269i	$-0.629587\pi$
$769$	14.4842	−	14.4842i	0.522312	−	0.522312i	0.918269	+	0.395957i	$0.129587\pi$
$770$		−	0.426909i		−	0.0153847i
$771$	−14.7998	−	22.2704i	−0.533001	−	0.802049i
$772$	−1.39097	−	0.372710i	−0.0500622	−	0.0134141i
$773$	8.74973	−	2.34448i	0.314706	−	0.0843252i	−0.0980088	−	0.995186i	$-0.531247\pi$
$773$	8.74973	−	2.34448i	0.314706	−	0.0843252i	0.412715	+	0.910860i	$0.364581\pi$
$774$	26.0429	+	3.56186i	0.936094	+	0.128029i
$775$	−6.99444	−	6.99444i	−0.251248	−	0.251248i
$776$			0.472084i			0.0169468i
$777$	−0.358462	−	0.177895i	−0.0128597	−	0.00638194i
$778$	−10.3284	−	10.3284i	−0.370292	−	0.370292i
$779$	5.06185	−	8.76738i	0.181360	−	0.314124i
$780$	−4.25991	−	21.0768i	−0.152529	−	0.754671i
$781$	21.0135	+	36.3965i	0.751923	+	1.30237i
$782$	−0.917267	+	3.42329i	−0.0328014	+	0.122416i
$783$	−40.7678	−	14.1824i	−1.45692	−	0.506839i
$784$	−6.06147	−	3.49959i	−0.216481	−	0.124986i
$785$	8.57914	−	32.0178i	0.306203	−	1.14276i
$786$	−10.0162	−	29.7522i	−0.357266	−	1.06122i
$787$	−4.89695	+	18.2757i	−0.174558	+	0.651458i	0.822069	+	0.569388i	$0.192820\pi$
$787$	−4.89695	+	18.2757i	−0.174558	+	0.651458i	−0.996627	+	0.0820699i	$0.973847\pi$
$788$	1.07594	+	4.01546i	0.0383288	+	0.143045i
$789$	1.37516	+	21.8210i	0.0489570	+	0.776847i
$790$	−8.40604	−	4.85323i	−0.299074	−	0.172670i
$791$	−0.0160161	−	0.00429150i	−0.000569467	−	0.000152588i
$792$	−10.3958	+	7.89431i	−0.369400	+	0.280512i
$793$	−0.0300562	−	0.0714299i	−0.00106733	−	0.00253655i
$794$	−2.58388	+	1.49180i	−0.0916983	+	0.0529421i
$795$	19.9764	−	22.6636i	0.708491	−	0.803796i
$796$	2.06042			0.0730295
$797$	16.8536	+	29.1913i	0.596986	+	1.03401i	0.993263	+	0.115879i	$0.0369685\pi$
$797$	16.8536	+	29.1913i	0.596986	+	1.03401i	−0.396277	+	0.918131i	$0.629698\pi$
$798$	−0.0942403	+	0.0317264i	−0.00333607	+	0.00112310i
$799$	−3.81090	+	3.81090i	−0.134820	+	0.134820i
$800$	1.77443	+	6.62226i	0.0627355	+	0.234132i
$801$	−20.6855	+	26.6792i	−0.730888	+	0.942663i
$802$	5.53740	−	9.59106i	0.195533	−	0.338672i
$803$	20.1130	−	34.8368i	0.709773	−	1.22936i
$804$	1.55118	−	0.522210i	0.0547058	−	0.0184169i
$805$	−0.0448757	−	0.0259090i	−0.00158166	−	0.000913171i
$806$	−3.14371	+	4.14473i	−0.110732	+	0.145992i
$807$	1.70668	+	27.0814i	0.0600778	+	0.953312i
$808$	−1.42114	−	5.30377i	−0.0499956	−	0.186586i
$809$	−9.20764	+	5.31603i	−0.323723	+	0.186902i	−0.653051	−	0.757314i	$-0.726511\pi$
$809$	−9.20764	+	5.31603i	−0.323723	+	0.186902i	0.329328	+	0.944216i	$0.393178\pi$
$810$	29.8511	+	8.32105i	1.04886	+	0.292372i
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	−0.559874	−	0.828578i	$-0.689151\pi$
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	0.828578	+	0.559874i	$0.189151\pi$
$812$	0.167375	+	0.167375i	0.00587371	+	0.00587371i
$813$	28.0999	−	9.45995i	0.985507	−	0.331775i
$814$	−34.0782	+	9.13123i	−1.19444	+	0.320049i
$815$	33.0526	−	19.0829i	1.15778	−	0.668446i
$816$	−5.16680	+	10.4112i	−0.180874	+	0.364465i
$817$	17.0515	−	4.56894i	0.596557	−	0.159847i
$818$	14.6788			0.513233
$819$	0.218065	+	0.217819i	0.00761981	+	0.00761121i
$820$	17.3013			0.604189
$821$	14.8427	−	3.97709i	0.518013	−	0.138801i	0.00966583	−	0.999953i	$-0.496923\pi$
$821$	14.8427	−	3.97709i	0.518013	−	0.138801i	0.508347	+	0.861152i	$0.330257\pi$
$822$	28.8957	−	1.82101i	1.00785	−	0.0635151i
$823$	13.1817	−	7.61045i	0.459485	−	0.265284i	−0.252343	−	0.967638i	$-0.581201\pi$
$823$	13.1817	−	7.61045i	0.459485	−	0.265284i	0.711828	+	0.702354i	$0.247868\pi$
$824$	−4.04193	+	1.08303i	−0.140807	+	0.0377292i
$825$	−10.2074	+	50.6505i	−0.355376	+	1.76342i
$826$	0.288307	+	0.288307i	0.0100315	+	0.0100315i
$827$	16.9790	−	16.9790i	0.590418	−	0.590418i	−0.347326	−	0.937744i	$-0.612910\pi$
$827$	16.9790	−	16.9790i	0.590418	−	0.590418i	0.937744	+	0.347326i	$0.112910\pi$
$828$	0.198911	+	1.57189i	0.00691265	+	0.0546269i
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	−0.732335	−	0.680944i	$-0.761570\pi$
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	0.223547	+	0.974693i	$0.428236\pi$
$830$	−13.0915	−	48.8583i	−0.454414	−	1.69590i
$831$	−28.2066	+	18.7447i	−0.978477	+	0.650247i
$832$	3.32333	−	1.39839i	0.115216	−	0.0484803i
$833$	−40.6750	−	23.4837i	−1.40930	−	0.813662i
$834$	1.73990	−	8.63361i	0.0602477	−	0.298957i
$835$	−25.6939	+	44.5031i	−0.889174	+	1.54009i
$836$	−4.38330	+	7.59210i	−0.151600	+	0.262578i
$837$	−3.26506	−	6.74866i	−0.112857	−	0.233268i
$838$	−7.28940	−	27.2044i	−0.251808	−	0.939761i
$839$	16.7213	−	16.7213i	0.577282	−	0.577282i	−0.356871	−	0.934154i	$-0.616156\pi$
$839$	16.7213	−	16.7213i	0.577282	−	0.577282i	0.934154	+	0.356871i	$0.116156\pi$
$840$	−0.127484	−	0.112369i	−0.00439862	−	0.00387709i
$841$	20.0028	+	34.6459i	0.689752	+	1.19469i
$842$	−7.27909			−0.250854
$843$	−16.9124	−	50.2368i	−0.582495	−	1.73025i
$844$	16.5841	−	9.57481i	0.570847	−	0.329579i
$845$	−21.9462	+	39.0129i	−0.754972	+	1.34208i
$846$	−0.933225	+	2.22136i	−0.0320849	+	0.0763719i
$847$	0.218335	+	0.0585027i	0.00750208	+	0.00201018i
$848$	4.38699	+	2.53283i	0.150650	+	0.0869778i
$849$	34.0715	−	22.6422i	1.16933	−	0.777079i
$850$	11.9071	+	44.4381i	0.408412	+	1.52421i
$851$	−1.10834	+	4.13640i	−0.0379935	+	0.141794i
$852$	16.3998	+	3.30500i	0.561849	+	0.113227i
$853$	−14.8432	+	55.3955i	−0.508221	+	1.89671i	−0.0706986	+	0.997498i	$0.522523\pi$
$853$	−14.8432	+	55.3955i	−0.508221	+	1.89671i	−0.437522	+	0.899208i	$0.644144\pi$
$854$	−0.000530397	0	0.000306225i	−1.81498e−5	0	1.04788e-5i
$855$	20.6474	−	2.61277i	0.706125	−	0.0893550i
$856$	0.852446	−	3.18137i	0.0291360	−	0.108737i
$857$	9.63613	+	16.6903i	0.329164	+	0.570129i	0.982346	−	0.187072i	$-0.0598998\pi$
$857$	9.63613	+	16.6903i	0.329164	+	0.570129i	−0.653182	+	0.757201i	$0.726566\pi$
$858$	27.1202	+	1.69374i	0.925867	+	0.0578233i
$859$	−21.1198	+	36.5805i	−0.720597	+	1.24811i	0.240164	+	0.970732i	$0.422799\pi$
$859$	−21.1198	+	36.5805i	−0.720597	+	1.24811i	−0.960761	+	0.277378i	$0.910534\pi$
$860$	21.3326	+	21.3326i	0.727437	+	0.727437i
$861$	−0.206543	+	0.137258i	−0.00703897	+	0.00467774i
$862$		−	18.9536i		−	0.645563i
$863$	4.51248	+	4.51248i	0.153607	+	0.153607i	0.779727	−	0.626120i	$-0.215358\pi$
$863$	4.51248	+	4.51248i	0.153607	+	0.153607i	−0.626120	+	0.779727i	$0.715358\pi$
$864$	−0.378924	+	5.18232i	−0.0128913	+	0.176306i
$865$	−63.3927	+	16.9860i	−2.15542	+	0.577542i
$866$	−30.4438	−	8.15738i	−1.03452	−	0.277199i
$867$	−21.5819	+	43.4879i	−0.732960	+	1.47693i
$868$			0.0411120i			0.00139543i
$869$	8.67331	−	8.67331i	0.294222	−	0.294222i
$870$	−27.4202	−	41.2613i	−0.929632	−	1.39889i
$871$	−3.15500	−	1.28623i	−0.106903	−	0.0435821i
$872$		−	7.64122i		−	0.258764i
$873$	0.535393	+	1.31115i	0.0181203	+	0.0443758i
$874$	0.532043	+	0.921525i	0.0179966	+	0.0311711i
$875$	−0.182086			−0.00615563
$876$	−5.10897	−	15.1757i	−0.172616	−	0.512740i
$877$	11.6623	+	3.12491i	0.393808	+	0.105521i	0.450288	−	0.892883i	$-0.351321\pi$
$877$	11.6623	+	3.12491i	0.393808	+	0.105521i	−0.0564803	+	0.998404i	$0.517988\pi$
$878$	−12.4481	−	3.33545i	−0.420102	−	0.112566i
$879$	12.2054	+	36.2551i	0.411679	+	1.22286i
$880$	−14.9821			−0.505046
$881$	−23.1313	−	40.0646i	−0.779314	−	1.34981i	−0.932337	−	0.361589i	$-0.882234\pi$
$881$	−23.1313	−	40.0646i	−0.779314	−	1.34981i	0.153023	−	0.988223i	$-0.451099\pi$
$882$	−20.8039	−	2.84533i	−0.700503	−	0.0958071i
$883$			5.00836i			0.168545i	0.996443	+	0.0842723i	$0.0268566\pi$
$883$			5.00836i			0.168545i	−0.996443	+	0.0842723i	$0.973143\pi$
$884$	22.3009	−	9.38375i	0.750061	−	0.315610i
$885$	−47.2320	−	71.0736i	−1.58769	−	2.38911i
$886$	8.90127	−	8.90127i	0.299044	−	0.299044i
$887$		−	21.6986i		−	0.728567i	−0.931288	−	0.364284i	$-0.881314\pi$
$887$		−	21.6986i		−	0.728567i	0.931288	−	0.364284i	$-0.118686\pi$
$888$	−6.24310	+	12.5800i	−0.209505	+	0.422156i
$889$	−0.272138	−	0.0729193i	−0.00912723	−	0.00244563i
$890$	−37.4265	+	10.0284i	−1.25454	+	0.336153i
$891$	−19.9201	+	33.7154i	−0.667350	+	1.12951i
$892$	18.6817	+	18.6817i	0.625509	+	0.625509i
$893$			1.61815i			0.0541494i
$894$	−7.62723	+	5.06867i	−0.255093	+	0.169522i
$895$	−58.6932	−	58.6932i	−1.96190	−	1.96190i
$896$	0.0142473	−	0.0246771i	0.000475970	−	0.000824403i
$897$	1.82396	−	2.74802i	0.0609001	−	0.0917536i
$898$	2.25983	+	3.91414i	0.0754115	+	0.130616i
$899$	−3.10202	+	11.5769i	−0.103458	+	0.386111i
$900$	12.4386	+	16.3801i	0.414620	+	0.546003i
$901$	29.4385	+	16.9963i	0.980740	+	0.566230i
$902$	−5.65867	+	21.1185i	−0.188413	+	0.703167i
$903$	−0.423908	−	0.0854286i	−0.0141068	−	0.00284289i
$904$	−0.150607	+	0.562074i	−0.00500912	+	0.0186943i
$905$	−1.03827	−	3.87486i	−0.0345131	−	0.128805i
$906$	−14.0460	+	9.33427i	−0.466647	+	0.310110i
$907$	26.6615	+	15.3930i	0.885282	+	0.511118i	0.872396	−	0.488799i	$-0.162565\pi$
$907$	26.6615	+	15.3930i	0.885282	+	0.511118i	0.0128856	+	0.999917i	$0.495898\pi$
$908$	−4.95918	−	1.32881i	−0.164576	−	0.0440981i
$909$	−9.96208	−	13.1188i	−0.330421	−	0.435124i
$910$	0.0481342	+	0.350464i	0.00159563	+	0.0116178i
$911$	13.1044	−	7.56582i	0.434168	−	0.250667i	−0.266953	−	0.963710i	$-0.586017\pi$
$911$	13.1044	−	7.56582i	0.434168	−	0.250667i	0.701120	+	0.713043i	$0.252684\pi$
$912$	1.11342	+	3.30730i	0.0368689	+	0.109516i
$913$	63.9194			2.11542
$914$	−5.08543	−	8.80823i	−0.168211	−	0.291350i
$915$	0.0961612	+	0.0847596i	0.00317899	+	0.00280207i
$916$	−5.61498	+	5.61498i	−0.185524	+	0.185524i
$917$	0.133669	+	0.498859i	0.00441414	+	0.0164738i
$918$	−2.54274	+	34.7755i	−0.0839228	+	1.14776i
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.0323673	+	0.999476i	$0.510305\pi$
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.849388	+	0.527769i	$0.823029\pi$
$920$	−0.909258	+	1.57488i	−0.0299773	+	0.0519223i
$921$	1.45069	−	7.19850i	0.0478017	−	0.237199i
$922$	23.5621	+	13.6036i	0.775977	+	0.448011i
$923$	−21.3544	−	27.5098i	−0.702890	−	0.905497i
$924$	0.178856	−	0.118858i	0.00588392	−	0.00391016i
$925$	14.3875	+	53.6950i	0.473059	+	1.76548i
$926$	−10.2633	+	5.92551i	−0.337272	+	0.194724i
$927$	−9.99769	+	7.59197i	−0.328367	+	0.249353i
$928$	5.87391	−	5.87391i	0.192821	−	0.192821i
$929$	37.9968	+	37.9968i	1.24663	+	1.24663i	0.957197	+	0.289436i	$0.0934677\pi$
$929$	37.9968	+	37.9968i	1.24663	+	1.24663i	0.289436	+	0.957197i	$0.406532\pi$
$930$	1.69989	−	8.43507i	0.0557414	−	0.276597i
$931$	−13.6213	+	3.64981i	−0.446419	+	0.119618i
$932$	−0.208135	+	0.120167i	−0.00681769	+	0.00393619i
$933$	−52.3080	+	3.29646i	−1.71249	+	0.107921i
$934$	0.594893	−	0.159401i	0.0194655	−	0.00521576i
$935$	−100.536			−3.28787
$936$	7.64421	−	7.65285i	0.249859	−	0.250141i
$937$	−2.41921			−0.0790323			−0.0395162	−	0.999219i	$-0.512582\pi$
$937$	−2.41921			−0.0790323			−0.0395162	+	0.999219i	$0.512582\pi$
$938$	−0.0260088	+	0.00696905i	−0.000849219	+	0.000227548i
$939$	−25.7681	+	51.9231i	−0.840909	+	1.69445i
$940$	−2.39492	+	1.38271i	−0.0781135	+	0.0450989i
$941$	−0.0432503	+	0.0115889i	−0.00140992	+	0.000377786i	−0.259524	−	0.965737i	$-0.583566\pi$
$941$	−0.0432503	+	0.0115889i	−0.00140992	+	0.000377786i	0.258114	+	0.966114i	$0.416899\pi$
$942$	15.8026	−	5.32001i	0.514876	−	0.173335i
$943$	1.87650	+	1.87650i	0.0611072	+	0.0611072i
$944$	10.1180	−	10.1180i	0.329311	−	0.329311i
$945$	−0.481509	−	0.167509i	−0.0156635	−	0.00544907i
$946$	−33.0163	+	19.0620i	−1.07345	+	0.619759i
$947$	−6.08611	−	22.7137i	−0.197772	−	0.738095i	−0.991532	−	0.129864i	$-0.958546\pi$
$947$	−6.08611	−	22.7137i	−0.197772	−	0.738095i	0.793760	−	0.608231i	$-0.208121\pi$
$948$	−0.307096	−	4.87298i	−0.00997400	−	0.158267i
$949$	−12.5836	+	30.8665i	−0.408481	+	1.00197i
$950$	11.9624	+	6.90651i	0.388112	+	0.224077i
$951$	−18.3176	+	6.16671i	−0.593990	+	0.199969i
$952$	0.0956054	−	0.165593i	0.00309859	−	0.00536691i
$953$	−13.8021	+	23.9060i	−0.447095	+	0.774392i	−0.998196	−	0.0600474i	$-0.980875\pi$
$953$	−13.8021	+	23.9060i	−0.447095	+	0.774392i	0.551100	+	0.834439i	$0.314208\pi$
$954$	15.0568	+	2.05931i	0.487483	+	0.0666725i
$955$	10.3061	+	38.4627i	0.333496	+	1.24462i
$956$	−4.75542	+	4.75542i	−0.153801	+	0.153801i
$957$	59.3328	−	19.9746i	1.91796	−	0.645688i
$958$	−10.0202	−	17.3554i	−0.323737	−	0.560729i
$959$	−0.476318			−0.0153811
$960$	−3.94350	+	4.47397i	−0.127276	+	0.144397i
$961$	25.0440	−	14.4592i	0.807871	−	0.466425i
$962$	26.9464	−	11.3385i	0.868788	−	0.365567i
$963$	−1.24045	−	9.80263i	−0.0399730	−	0.315885i
$964$	−25.0664	−	6.71652i	−0.807335	−	0.216325i
$965$	−4.29410	−	2.47920i	−0.138232	−	0.0798083i
$966$	−0.00163943	−	0.0260144i	−5.27478e−5	−	0.000836999i
$967$	−8.31034	−	31.0146i	−0.267243	−	0.997363i	−0.960863	−	0.277023i	$-0.910652\pi$
$967$	−8.31034	−	31.0146i	−0.267243	−	0.997363i	0.693621	−	0.720340i	$-0.256014\pi$
$968$	2.05311	−	7.66231i	0.0659895	−	0.246276i
$969$	7.47148	+	22.1933i	0.240019	+	0.712953i
$970$	−0.420710	+	1.57011i	−0.0135082	+	0.0504132i
$971$	16.6187	+	9.59478i	0.533318	+	0.307911i	0.742366	−	0.669994i	$-0.233703\pi$
$971$	16.6187	+	9.59478i	0.533318	+	0.307911i	−0.209049	+	0.977905i	$0.567037\pi$
$972$	4.82488	+	14.8230i	0.154758	+	0.475447i
$973$	−0.0375004	+	0.139953i	−0.00120221	+	0.00448670i
$974$	10.5733	+	18.3135i	0.338791	+	0.586804i
$975$	2.66872	−	42.7316i	0.0854676	−	1.36851i
$976$	−0.0107467	+	0.0186139i	−0.000343995	+	0.000595817i
$977$	21.6436	+	21.6436i	0.692440	+	0.692440i	0.962768	−	0.270328i	$-0.0871321\pi$
$977$	21.6436	+	21.6436i	0.692440	+	0.692440i	−0.270328	+	0.962768i	$0.587132\pi$
$978$	17.1973	+	8.53456i	0.549909	+	0.272905i
$979$		−	48.9637i		−	1.56489i
$980$	−17.0412	−	17.0412i	−0.544360	−	0.544360i
$981$	−8.66595	−	21.2225i	−0.276683	−	0.677583i
$982$	19.0783	−	5.11201i	0.608812	−	0.163131i
$983$	−21.8828	−	5.86347i	−0.697952	−	0.187016i	−0.107639	−	0.994190i	$-0.534329\pi$
$983$	−21.8828	−	5.86347i	−0.697952	−	0.187016i	−0.590313	+	0.807175i	$0.700996\pi$
$984$	4.81698	+	7.24849i	0.153560	+	0.231073i
$985$			14.3139i			0.456079i
$986$	39.4163	−	39.4163i	1.25527	−	1.25527i
$987$	0.0176209	−	0.0355065i	0.000560880	−	0.00113018i
$988$	2.74239	−	6.72684i	0.0872470	−	0.214009i
$989$			4.62747i			0.147145i
$990$	−41.6108	+	16.9913i	−1.32248	+	0.540018i
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	−0.995997	−	0.0893845i	$-0.971510\pi$
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	0.420589	−	0.907251i	$-0.361823\pi$
$992$	1.44280			0.0458089
$993$	−7.02867	−	1.41646i	−0.223048	−	0.0449500i
$994$	−0.265846	−	0.0712333i	−0.00843213	−	0.00225938i
$995$	6.85276	+	1.83619i	0.217247	+	0.0582111i
$996$	16.8245	−	19.0877i	0.533106	−	0.604818i
$997$	−17.7685			−0.562733			−0.281366	−	0.959600i	$-0.590788\pi$
$997$	−17.7685			−0.562733			−0.281366	+	0.959600i	$0.590788\pi$
$998$	2.65476	+	4.59817i	0.0840348	+	0.145553i
$999$	−3.07241	+	42.0196i	−0.0972069	+	1.32944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.41.2	yes	56
3.2	odd	2		702.2.bc.a.665.8		56
9.2	odd	6		234.2.y.a.119.3	yes	56
9.7	even	3		702.2.bb.a.197.8		56
13.7	odd	12		234.2.y.a.59.3	✓	56
39.20	even	12		702.2.bb.a.449.8		56
117.7	odd	12		702.2.bc.a.683.8		56
117.20	even	12	inner	234.2.z.a.137.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.3	✓	56	13.7	odd	12
234.2.y.a.119.3	yes	56	9.2	odd	6
234.2.z.a.41.2	yes	56	1.1	even	1	trivial
234.2.z.a.137.2	yes	56	117.20	even	12	inner
702.2.bb.a.197.8		56	9.7	even	3
702.2.bb.a.449.8		56	39.20	even	12
702.2.bc.a.665.8		56	3.2	odd	2
702.2.bc.a.683.8		56	117.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.958654 - 1.44256i) q^{3} +(0.866025 - 0.500000i) q^{4} +(3.32591 - 0.891175i) q^{5} +(1.29935 + 1.14529i) q^{6} +(-0.0201488 - 0.0201488i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.16197 + 2.76583i) q^{9} +(-2.98193 + 1.72162i) q^{10} +(-1.12616 - 4.20290i) q^{11} +(-1.55150 - 0.769968i) q^{12} +(1.39839 + 3.32333i) q^{13} +(0.0246771 + 0.0142473i) q^{14} +(-4.47397 - 3.94350i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.35521 - 5.81139i) q^{17} +(0.406522 - 2.97233i) q^{18} +(-0.521462 - 1.94612i) q^{19} +(2.43473 - 2.43473i) q^{20} +(-0.00975013 + 0.0483815i) q^{21} +(2.17558 + 3.76822i) q^{22} +0.528142 q^{23} +(1.69792 + 0.342174i) q^{24} +(5.93735 - 3.42793i) q^{25} +(-2.21088 - 2.84816i) q^{26} +(5.10381 - 0.975270i) q^{27} +(-0.0275237 - 0.00737496i) q^{28} +(-7.19404 - 4.15348i) q^{29} +(5.34218 + 2.65118i) q^{30} +(-0.373424 - 1.39364i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-4.98334 + 5.65369i) q^{33} +(-1.73678 + 6.48176i) q^{34} +(-0.0849690 - 0.0490569i) q^{35} +(0.376625 + 2.97627i) q^{36} +(-2.09857 + 7.83198i) q^{37} +(1.00739 + 1.74484i) q^{38} +(3.45354 - 5.20318i) q^{39} +(-1.72162 + 2.98193i) q^{40} +(3.55302 + 3.55302i) q^{41} +(-0.00310415 - 0.0492564i) q^{42} +8.76179i q^{43} +(-3.07674 - 3.07674i) q^{44} +(-1.39975 + 10.2344i) q^{45} +(-0.510146 + 0.136693i) q^{46} +(-0.775777 - 0.207869i) q^{47} +(-1.72862 + 0.108938i) q^{48} -6.99919i q^{49} +(-4.84783 + 4.84783i) q^{50} +(-11.5998 + 0.731018i) q^{51} +(2.87270 + 2.17889i) q^{52} +5.06566i q^{53} +(-4.67748 + 2.26300i) q^{54} +(-7.49104 - 12.9749i) q^{55} +0.0284946 q^{56} +(-2.30750 + 2.61790i) q^{57} +(8.02391 + 2.15000i) q^{58} +(13.8214 + 3.70343i) q^{59} +(-5.84632 - 1.17819i) q^{60} -0.0214935 q^{61} +(0.721399 + 1.24950i) q^{62} +(0.0791403 - 0.0323159i) q^{63} -1.00000i q^{64} +(7.61257 + 9.80688i) q^{65} +(3.35025 - 6.75082i) q^{66} +(-0.668189 + 0.668189i) q^{67} -6.71041i q^{68} +(-0.506305 - 0.761877i) q^{69} +(0.0947706 + 0.0253937i) q^{70} +(-9.32969 + 2.49988i) q^{71} +(-1.13411 - 2.77737i) q^{72} +(6.53713 + 6.53713i) q^{73} -8.10826i q^{74} +(-10.6369 - 5.27880i) q^{75} +(-1.42466 - 1.42466i) q^{76} +(-0.0619924 + 0.107374i) q^{77} +(-1.98918 + 5.91973i) q^{78} +(1.40950 + 2.44132i) q^{79} +(0.891175 - 3.32591i) q^{80} +(-6.29967 - 6.42761i) q^{81} +(-4.35155 - 2.51237i) q^{82} +(-3.80210 + 14.1896i) q^{83} +(0.0157469 + 0.0467747i) q^{84} +(5.98015 - 22.3182i) q^{85} +(-2.26772 - 8.46324i) q^{86} +(0.904943 + 14.3596i) q^{87} +(3.76822 + 2.17558i) q^{88} +(10.8696 + 2.91249i) q^{89} +(-1.29681 - 10.2480i) q^{90} +(0.0387852 - 0.0951367i) q^{91} +(0.457384 - 0.264071i) q^{92} +(-1.65242 + 1.87470i) q^{93} +0.803143 q^{94} +(-3.46867 - 6.00791i) q^{95} +(1.64153 - 0.552626i) q^{96} +(0.333814 - 0.333814i) q^{97} +(1.81152 + 6.76070i) q^{98} +(12.9331 + 1.76884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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